How to Use Free English Lessons on Line

How to Use Free English Lessons on LineFree English lessons online can be a great thing. Just like the old days when the only ways to learn a new language were by classroom or books at a store. So what I'm going to share with you here is my experience about where to get free English lessons online.The best way to start is with grammar. The more basic and common grammar is easy to learn. Grammar is not the only key skill to build a solid foundation with.Vocabulary can be easily learned when using grammatical words. However, when learning vocabulary in the first months it can be overwhelming. In other words, a beginning language student should not start writing as well.An example would be if you're learning German. Start by looking for someone who speaks the language at the local bookstore. Now that you know how to write and speak a language, then you can look for native speakers that speak German.Since English has many words that can be used in many different situations in daily life, it would be easy to pick up more words as you go along. However, there are many new words as well. A lot of these new words you can actually say out loud and in actual usage.Although most learners with a solid grasp of English to learn English from books, you should take advantage of free lessons on line. Many sites offer English lessons free of charge. This may not be the best way to learn, but it will certainly save money on the initial cost of textbooks.It's quite easy to make mistakes with grammar and the rules of English, but learning to write and speak the language can be easier. Try to pick a native speaker to discuss a topic with. This will help build a better foundation for your English learning.Getting to a point where you can speak good English is important, so make sure that you use these free resources to build a better foundation. Eventually you can build up more lessons on site and purchase books that are more advanced and expensive. For now, all you need is practice and an English beginner to help you.

Study Gate Online With Ease

Study Gate Online With EaseThere are many ways to study gate online. All you need is an internet connection and you will be able to read books in any language you choose and do online projects which would help you prepare for your exams.You can also learn study gate online if you are an employee. There are so many companies who are using this method to learn a lot about their employees. They will be able to monitor your progress and the overall performance of your coworkers. They will also have access to important information regarding the performance of your fellow workers.A more effective way to learn is when you're on vacation or taking a break from work. There are some companies who offer online tutoring to their employees on their company computers. These programs allow you to learn anything that you want at your own pace. You can even try out your language skills while in your vacation or break.In most cases, the online tutoring programs are for free and offer a large library o f free materials. The costs can vary according to the materials you would like to use and the features you would like to use.When choosing an online tutoring program, it is important to decide how many hours of study you would like to take. If you do not know what hours are required, simply look around online and find a course that would fit in with your schedule. It would also be better if you do not hire a tutor for the whole day because it will not allow you enough time to do your homework or work on assignments.You can also look online for free online resources that will help you learn more about learning gate online. You can find links to e-books that would teach you many different subjects like English language, music and many more.Tstudy gate online tutoring In conclusion, there are many ways to study gate online. With enough motivation and time, you would be able to master this new skill to prepare for your examinations.

GED Tutoring In Ohio

GED Tutoring In OhioDo you want to learn GED? There are many places that offer GED tutoring in Ohio.If you are looking for a place to take the GED exam, you can either get it done at a local high school or local college. You could also opt to take the GED and then study at your own pace. Both options can work out well.To get the GED, you need to complete several different courses. One of the most important courses you will need to complete is the Advanced Placement course. This is offered by many high schools, colleges, and community colleges across the country. Once you have taken this course, you will be ready to take the GED test.You will have to take the GED test within one year of completing your course. This is a two hour long test and is often used as a pre-test to determine what you will need to do once you take the GED test.Since many colleges in Ohio do not offer the GED exam, some people choose to take the GED test from the comfort of their own home. These courses typicall y last eight weeks. You will have to take the tests four times a year.If you have taken a test like the GED and are not satisfied with the results, you may take the GED retest. You will have to submit your test scores to the test board. The results will be sent to you via mail or in person. Your scores will be held until you have finished your high school program.If you want to learn more about the exam and about GED tutoring in Ohio, you should speak with a counselor. There are many GED tutors in Ohio who will help you through the process. The sooner you get started, the sooner you will be on your way to becoming an American citizen.

Solving Radical Equations

Solving Radical Equations The meaning for the word radical is root. Radical equations is an equations which can contain constants, variables and radical included in them. Radicals can be simplified and solved. There are different mathematical operations that can be used to simplify and solve questions related to radicals. Two radicals can be added or subtracted if they have the same number or expression in the root, this makes them similar radicals to carry mathematical operations. Example 1: Simplify and find the answer for the given equation 102x + 52x 92x? Solution: The given question is on adding and subtracting radicals. This question contains the adding and subtracting the similar radical terms containing 2 with variable x. The first step of the question is solving for 10 2x + 5 2x = 15 2x Now subtract 9 2x from the earlier answer 15 2x. This makes 15 2x 9 2x = 6 2x Therefore simplifying the radicals gives 10 2 x + 5 2x 9 2x = 6 2x Hence solution = 62x. Example 2: Simplify find the answer for the given question 12 5x + 10 5x 35x? Solution: The given question is on adding and subtracting radicals. This question contains the adding and subtracting the similar radical terms containing 5 with variable x. The first step of the question is solving for 12 5x + 10 5x = 22 5x Now subtract 35x from the earlier answer 225x This makes 225x 35x = 195x. Therefore simplifying the radicals gives 125x + 105x 35x = 195x. Hence solution = 195x.

How to Prepare for the College Search

How to Prepare for the College Search High school students have a lot going on already, but when you add on the big college search, its hard for a student not to find life extremely overwhelming. This is one giant process that requires a lot of guidance, so it is critical that a student really understands what theyre getting into before taking on this life-changing project. It cannot be treated as something they will coast their way through or just occasionally check on. The college search should be an extremely organized endeavor that you are keeping up with every day and giving very careful attention to. Of course, this takes us back to the overwhelming aspect. How can a high school student get through this successfully without getting completely freaked out? Well, that is why beginning this process way ahead of time is so important. Far too many students leave this search until early senior year, which frankly, is nowhere near enough time to make informed decisions on which schools youd like to attend. Yes, this is a good time to literally get your applications in, but you should have your choices picked out and researched well before then. Waiting too long will not only drastically limit your time to complete your applications successfully, it will put unnecessary extra pressure on you to make a decision quickly too quickly. Having to choose a school in a rushed manner is one of the worst positions a student can be in. So why wouldnt you start looking into this far ahead of time? This is one of the biggest decisions of a young students life, and one of the most exciting; there should be no reason you wouldnt want to begin looking into this very early on. One of the most important ways to guarantee an easier time deciding between your future acceptance letters is to make sure you are only applying to schools you know you would love to attend. There are plenty of things that need to be looked into. On one hand, you must evaluate all the aspects of the school that appeal to you personally the town, the programs, the dorm life, the clubs/sports, etc. On the other hand, it is equally necessary to look into the requirements this school demands of their applicants GPAs, ACT/SAT scores, leadership, etc. Another key reason to look into this search with plenty of time to spare is that you may need some time to improve your credentials. Perhaps there is a school that you love everything about, but that also requires an ACT score above what you have. Giving yourself a chance to shoot up that score will benefit you greatly youll be very let-down if you find you have no chance of getting into that school just because you didnt think about requi red test scores earlier on in high school. If you dont research various colleges requirements early on, you wont know what youre reaching for as you go through your high school career. Once youve given yourself enough time to know what kinds of scores, grades, and clubs you must incorporate into your life, you must also use this time to determine which schools actually offer the things you want personally. Visit the campuses, read review books, research the websites, set up meetings with admissions counselors treat every approach to a school as if you are going to be enrolling in them tomorrow. Get a hold of every aspect of this schools culture that matters to you so you dont waste your time applying to a place that wouldnt really make you happy. In the end, you need to apply to schools that you know would be a fit for you and that you would have a solid chance of getting into. The worst thing you can do is waste your time with places that you are absolutely sure wont work out in either of those areas. This isnt to say that you should unnecessarily limit yourself; dont be afraid to apply to a university you love that may require a slightly higher GPA than you have. Remember, most college admissions officers look at applications holistically, so never write off your chances completely if there is just one tiny factor that doesnt perfectly match up with your qualifications. And finally, never apply to a school just because you feel like you should or because your best friend is. You will be very unhappy later if you end up at a school that you were told you would like, but dont actually like once you get there. In the end, this school is for you and you only. This is why you must look into everything yourself with a very meticulous approach and then decide on your own if you like it. You really cant avoid the exhausted feelings that will come out of this search. Any typical high school student will be inclined to skip over some of these steps and assume theyll be fine. But with enough time set aside and enough belief that this will pay off wonderfully later, this search can be completed with all the attention it deserves and leave you ultimately satisfied.

Learn Arabic for Educational Reasons

Learn Arabic for Educational Reasons The Educational Benefits of Learning the Arabic Language ChaptersLearning Arabic as a Second LanguageDeveloping Your Listening and Concentration Skills in your Arabic LessonsWhy Learn Arabic: Make Yourself Stand Out in Your Professional FieldThe Benefits of Learning Arabic: Learn About the World's Second Largest ReligionToday Arabic is spoken by more than 300 million people around the world.It's also the official language of the 22 Arab League nations and one of the 6 official languages used at the United Nations.So why should you learn Arabic?What can learning Arabic bring you in terms of your academic progress?Will learning Arabic help you find a better job? Will it open doors to new professional opportunities around the world?What are the real benefits of speaking this ancient language in the worlds of business, tourism, and science? From a cultural point of view, Arabic has made great contributions not only to Middle Eastern culture, but also to our own.By deciding to learn Arabic, whether its an 'Arabic for beginners' class  in school ,  or through private or even online lessons,  there are a number of advantages to speaking this language:It's the primary language spoken in the Arab world, and is the second language learned by all Muslims.It's the official language of more than 20 countries.It opens doors to Arab and Islamic culture.The opportunity to discover a formidable heritage of religious thinking, architecture, science, and philosophy that has inspired a number of civilizations in the Middle East and the West.Speaking Arabic will help you open your eyes to the world, to develop interpersonal skills, and to indulge your intellectual curiosity.It will also help you stand out from your academic peers and perhaps help you find a job that is truly interesting and desirable.What's more, it studying Arabic couldn't be easier. You can learn Arabic online, take Arabic courses at a local language school, or find a tutor on the Superprof website who can teach you how to speak Arabic, as well as how to master Arabic s cript and its grammatical structures.So, are you ready to make a difference in your academic career by learning the Arabic language?We're here to offer you some advice to get you started.After reading this article, you'll have everything you need to start learning Arabic.Don't force yourself to choose Arabic if you don't feel up to the task because you'll find yourself unable to put forth the necessary effort.But if you like the sound of Arabic, if you're already familiar with some Arabic vocabulary, and if Arabic grammar and reading don't scare you, go ahead!What You Should Know about the Basics of ArabicBefore anything else, you should know that there are two types of Arabic, which are known as literary Arabic and dialectal Arabic.Literary Arabic, also sometimes known as Modern Standard Arabic,  is the form of Arabic common to all Arab countries, and is the predominant written form, but it's also found in public discourse and in the media.Dialectal Arabic corresponds to the form o f Arabic used orally. This changes because the spoken forms of dialectal Arabic are different in each country; Egyptian Arabic has little in common with the Moroccan dialect or that of   Saudi Arabia.Some other basics about the Arabic language:Its alphabet uses 28 letters that change according to their place within words.It's read from right to left.There are fewer vowels.It has a particular syntax that applies to a strict word order: verb, subject, complement.Certain sounds are difficult to reproduce and so it's important to pay attention to gestures, facial expressions, and voice intonation during a conversation.Developing Your Listening and Concentration Skills in your Arabic LessonsThe Arabic language is one of the most widely spoken internationally.But if want to learn this unique language, you'll need to become an excellent listener, meaning not only will you need to learn the Arabic alphabet and learn some basics of Arabic calligraphy, you'll also need to train your ear to he ar these new sounds in Arabic, on a continually regular basis.Check here for an online Arabic course.Improve your concentration by learning Arabic.Immerse yourself entirely in Arabic by listening to speeches, discussions in Arabic,  Arabic speaking radio or even by watching the news on  Arabic language TV stations like Al-Jazeera.For those who want to learn Arabic on their own, there's also the option of listening to podcasts in Arabic, which are an excellent way to develop your listening skills and reinforce your concentration; with podcasts you can download them to listen over again, enrich your  vocabulary, learn the rules of  Arabic grammar, learn how to use proper intonation, and discover the  nuanced meanings of Arabic words.In sum, you'll boost your level of oral comprehension and improve your writing, reading, and pronunciation skills.Some tools to help you learn Arabic in addition to your lessons:Internet radio stations: when you're in the car, in traffic jams, on public tr ansport, on foot, on a plane... there are lots of different radio stations broadcasting live.Arabic language documentary films: there are lots of stations that specialize in showing documentaries in Arabic, covering a variety of thematic subjects such as politics, nature, culture, and the arts.Arabic language audio books: these allow you to learn about Arab culture with novels, stories, scientific non-fiction, etc.Educational websites: they'll have lots of recorded discussions or dialogues between Arabic speaking experts in a variety of fields.Why Learn Arabic: Make Yourself Stand Out in Your Professional FieldFew of your peers, in high school or university, will be able to develop such international experience during their studies.Few of them will have the chance to discover fantastic and mythical countries like Egypt, Jordan, and Lebanon, countries where the US and other Western countries have crucial interests (economic, financial, cultural, and religious).Learning Arabic will he lp you understand Arab cultureIn Arabic, the language and culture are closely linked. Your proficiency in one grows as it does in the other. Even from knowing some colloquial slang or a few keys phrases, your understanding of Arab culture will increase which will be an asset for any employer looking for staff to deal with middle eastern relationsThere is often a lack of mutual understanding of local contexts. Speaking and reading Arabic offers you the opportunity to participate in new business endeavours with a better understanding of complex political and cultural situations.Familiarity with the Arabic language and an understanding of the cultural differences within a particular context are more important than anything else when trying to meet the challenges of the Middle East and North Africa.The Benefits of Learning Arabic: Learn About the World's Second Largest ReligionIslam is the most widespread religion in the Arab world and it's through the Quran that believers share in thei r faith.It serves as a prism through which many Arabs see the world.Learning about the Quran will both help you better understand Islam and learn more Arabic vocabulary through its rich text, which is the source of many ideologies in the Arab world.By deciding to learn Arabic, you'll be able to better understand ancient traditions, learn about Islamic beliefs, become a better intercultural communicator, and establish better and lasting relationships with Arabic speakers and Muslim populations.Discover the mysteries of the Quran!As you can see, learning Arabic can prove itself difficult at first, but the benefits and impact on your academic and professional careers are undeniable.With the Internet, there are several ways to learn such as  night courses, free online Arabic lessons, private lessons, adult learning lessons at universities, and  Massive Open Online Courses (MOOC)  amongst others.Learn Arabic now and enhance your language comprehension skills, but more importantly augment your understanding of the world today.You will find arabic lessons london as well as across the country.

Should You Take the ACT Plus Writing

Should You Take the ACT Plus Writing Most high school students plan to take either the ACT or the SAT, but once you choose an exam, your decision is not yet complete. The ACT, for instance, offers an optional writing componentthe ACT Plus Writing. But should you take this sub-test? First, consider the basics The ACT Plus Writing lengthens the ACT by thirty minutes, and it currently costs an additional $16.50. You will be presented with a single prompt. This prompt will describe an issue and two opposing viewpoints. You must then support one of the two provided perspectives, or alternately, present your own. Of course, your score will not reflect the side you choose, and you do not have to argue for the viewpoint you actually holdjust the one about whichyou can write the most effectiveessay. The case for completing the ACT Plus Writing is fairly compelling: It may be required While the writing portion of the exam is technically optional, certain schools require it for admission. If you are sitting for the ACT during your junior year, you may have little idea about which colleges you will ultimately apply towhich means it may or may not be required. Some schools simply recommend that you take it - follow their advice. Colleges that do not require the ACT Plus Writing may still accept and examine your results, which couldstrengthen your portfolio. It can highlight key skills Though the ACT may feel like a mere means to an end, it is designed to allow you to showcase your skills to colleges. This is also true of the Writing section. By completing a short essay, you can demonstrate your communication skillsand schools are deeply interested in your ability to read, write, and thoughtfully argue. It is not multiple-choice The ACT Plus Writing is scored by two human readers. These individuals review and evaluate your essay, and then they assign it a score between 2 and 12. If you do not excel at multiple-choice testing, the ACT Plus Writing can be a wonderful way for you to stand out to colleges. You may also find these tips on how to improve your ACT scorehelpful. It may improve your ability to write well While studying for the ACT Plus Writing, you may realize that you are becoming a better writer. Often, the ability to write well is developed by continual practice. As you complete sample prompts, your skill set in writing quickly and clearly will improve. Writing tutors can also be of great use, as they can offer excellent feedback and direct your prep efforts accordingly. Remember thatACT practice testsmay help you improve your overall score as well. This will work to your advantage as you enter college, where you will be expected to write coherently startingthe first day of your first semester. Thus, sitting for the ACT Plus Writing may make you a more successful college studentif you prepare appropriately. If you plan to review for the other sections of the ACT, it may make logistical sense to proceed one step furtherin other words, to complete the ACT Plus Writing as well. While you might regret not taking it, it is unlikely that the reverse will be true. [RELATED: What is an Average ACT Score?]

How Higher Order Thinking Skills Lead to More Effective Problem Solving

How Higher Order Thinking Skills Lead to More Effective Problem Solving Solve Problems More Effectively Through Higher Order Thinking ChaptersWhat Is Thinking About?What Are Problems Solving Skills?How to Turn a Student into a Problem SolverThe Role of Problem-Solving in Higher Order ThinkingAs we all know, some problems have easy solutions and others require a bit more thought.By that, we obviously don’t mean thinking about a problem for a longer period of time while using the same parameters and variables.Problem-solving entails examining a situation from a variety of perspectives and with a host of different aspects to arrive at the best solution â€" not just for that problem but for the larger framework in which it manifested.What, exactly, are we talking about, here?We do not mean to infer that word problems in a math assignment represent the opportunity to apply problem-solving skills in the classroom.Such problems demand logical thinking, not critical thinking which leads to problem-solving.Who knew that there were so many different types of thinking involved in solving problems?This article examines the p remise of higher-order thinking, its component part called problem-solving and how critical thinking skills are vital to the effort.By asking the right questions, teachers are instrumental in helping student groups think Image by succo from Pixabaya single definition that wholly characterises thought.  Specialists in educational psychology are equally at loggerheads over the issue.Clearly, students must be given information â€" that is done by someone who is knowledgeable of facts... in other words, a teacher.Ideally, students would process that information, arrive at conclusions and connect concepts to form a knowledge base into which they will integrate new facts.Now things get a bit more tricky.Our school teachers are very good at imparting information. Given the chance, they would be equally adept at guiding students as they work with this information.The trouble is, in our current curriculum standards, there is usually only room for one learning activity: either presenting new information OR working with said information.Generally, the latter aspect of learning is relegated to homework assignments. In such instances, tutors are instrumental in helping students gain thinking skills.To be a problem solver, you must be an active listener! Image by Couleur from PixabayWhat Are Problems Solving Skills?Problems are opportunities in work clothes â€" Henry Kaiser, IndustrialistIn the workplace, problem-solving is generally defined as the ability to manage difficult situations and complex challenges.Do such situations exist in classrooms across the UK?As far as academics go, primary and secondary school students are usually not confronted with situations where they would need problem-solving skills.However, cultivating such abilities in the early stages of education would serve students well a bit later in life, perhaps at the undergraduate and graduate levels; and most certainly will impact their career goals.Thus, were students trained to solve problems as early as possible, it would benefit not just student learning but society as a whole.The question remains: if students are unlikely to encounter situations where problem-solving skills are needed, how should those skills be taught?Let’s break down exactly what problem-solving skills involve:Creativity â€" an aspect of student intellect that is unfortunately suppressed in the course of formal education.Communication: there is a distinct lack of opportunity for talking in class!Active listening â€" we hope our kids listen to their teachers but there is little chance in a group setting to practise active listening.Research and analysis: these skills play a limited role in classroom learning; they are more the purview of after-school assignmentsTeam building: in the current teacher-led instruction model, there is no place for this facet of problem-solving.Even under the current teaching demands, there is still room for teachers to help their students cultivate these skills.Do you know the difference between critical thinking and higher-order thinking?How to Turn a Student into a Problem SolverWe’re not taught how to think â€" Sasuke, university studentThis particular undergraduate student hit the nail on the head with her assertion.As far as our general education standards are concerned, a school teacher’s primary function is to push information and do their best to ensure high test scores.For educators, this is particularly galling because it appears that those aims and student achievement are mutually exclusive propositions if you consider that said achievement should mean that every student would become a critical thinker and problem solver.An effective way around that is to embrace active learning and creative thinking in everyday class activities.Teaching strategies could evolve to include asking open-ended questions which would challenge students’ comprehension of the material at hand.Naturally, inviting discussion would not necessarily work well in math and science classes; STEM facts are pretty much indisputable.  In such classes, a certain amount of memorization is necessary but the assigned work need not be a test of memory.For teachers of those subjects, group study would be an effective way to cement new knowledge. Furthermore, assigning project-based learning activities could have a formative influence on student learning.Here’s how such an assignment may look.Subject: math. The topic: percentages. The assignment: calculate a budget for a fictitious country.Students must first discuss what must be paid for: education, healthcare, environmental protection, civic matters such as road maintenance and policing, to name a few.Next, they would collectively calculate what percentage of funds should be allocated to each. The assignment culminates in a presentation of each group's proposed budget.Classroom activities such as these encourage students to think beyond their personal experiences and they elicit interest (who doesn’t l ike money!) all while making use of their newly-gained math skills.As for the educator in the room, s/he needs only to go from group to group, asking the types of questions that would stimulate further thought.Such a pedagogy is the trademark of a master teacher; it sets the stage for student engagement better than any teacher-centred methodology ever could!Allowing students to work as a team is a good way to build problem-solving skills Image by Alexas_Fotos from PixabayThe Role of Problem-Solving in Higher Order ThinkingWe described in a sister-article how higher-order thinking comprises of both critical thinking and problem-solving.The concept of higher order thinking itself has its roots in various learning taxonomies, among them Blooms Taxonomy.Benjamin Bloom, an American educational psychologist, theorised that learning follows a certain hierarchy determined by the complexity and specificity of what being learned.There is more than one way that we learn and, to make learning e ffective, all three domains should be addressed.Remember how we used the words affective, cognitive and psychomotor  earlier in this article?According to his theory, those are the three domains under which learning is classified.Applying this model, we see that psychomotor learning starts very early â€" in infancy, and then effective learning follows shortly after, as toddlers discover emotions and how to manage them.Cognitive learning really takes off once a child starts school; in fact, throughout a person’s academic career, this type of learning is the one that is overwhelmingly addressed while the other two domains are mostly ignored.That assertion poses a very serious question: if we do not teach students to reason according to emotional as well as intellectual knowledge, are we creating cognitive disparities that will ultimately affect how people function in society?Instructional strategies that incorporate both problem-solving and critical thinking would be an effective sol ution to that admittedly gloomy projection.Posing higher order thinking questions such as ‘Can you give me an example of...’ or ‘What is the difference between...’ takes students away from the mere spilling of facts on demand and smack into critical thinking territory.They draw on students’ prior knowledge and cause them to reflect on dissimilar or not-conspicuously related concepts.Let’s go back to our fictitious country budget example, only this time we project a student who has a severe medical condition that causes many trips to AE.As s/he reflects on the assignment, s/he remembers how many times s/he has taken ambulance rides and has had emergency medical treatment.Drawing on this experience, s/he would urge his group to include funds for emergency medical care into their budget â€" a facet of government budgeting that perhaps other students would not think to incorporate into their plan.This student and that group have moved beyond rote work. They are drawing on th eir multiple intelligences to complete that assignment most creatively.Later, as they share their work in class, other students could learn from their example, meaning that everyone enjoys enrichment!Meanwhile, the teacher may bask in the warm glow of being a knowledge facilitator...Tutors: know when to back off of a higher-order thinking exercise!

Combining Like Terms Worksheet

Combining Like Terms Worksheet Combining like terms worksheet consist of collection of problems where the like terms need to be added. Like terms combining is a tool to simplify an expression or equation by adding or subtracting. Two terms are like terms when they have same variable part having same degree. 6x and 7 are not like terms since 2nd term has no variable. 4x and 7x are like since variables match and degrees match. Now 3x^2 and 3x are not like terms since they have different degree but same variable. Worksheet indicates list of problems. Example 1: Simplify by combining like terms for the following a. 4x + 5x b. 3 + 5 + 6y + 3x c. 5x^3 + 5y + 5x + 4x^3 Solution: a. 4x + 5x = 9x b. 3 + 5 + 6y + 3x = (3 + 5) + 6y + 3x = 8 + 6y + 3x c. 5x^3 + 5y + 5x + 4x^3 = ( 5x^3 + 4x^3 ) + 5y + 5x = 9x^3 + 5y + 5x. Example 2: Simplify by combining like terms for the following a. 3x + 6y + 4x + 5x b. 6x^3 + 3y^2 + 5x + 4x^3 Solution: a. 3x + 6y + 4x + 5x = (3x + 4x + 5x) + 6y = 12x + 6y b. 6x^3 + 3y^2 + 5x + 4x^3 = (6x^3 + 4x^3) + 3y^2 + 5x = 10x^3 + 3y^2 + 5x.