Wednesday, September 28, 2016

Middle School Math Solutions – Polynomials Calculator, Multiplying Polynomials

Multiplying polynomials can be tricky because you have to pay attention to every term, not to mention it can be very messy. There are a few ways of multiplying polynomials, depending on how many terms are in each polynomial. In this post, we will focus on how to multiply two term polynomials and how to multiply two or more term polynomials.

Multiply two term polynomials

When multiplying polynomials with two terms, you use the FOIL method. The FOIL method only works for multiplying two term polynomials. FOIL stands for first, outer, inner, last. This lets you know the order of how to distribute and multiply the terms. Let’s see how it works.


After FOILing, multiply the terms, group like terms, and add like terms if there are any.
Here is another helpful identity to use when multiplying two term polynomials:
(a+b)(a-b)=a^2-b^2
Multiplying these polynomials is pretty simple because if you memorize these identities then you just plug in the values and have an answer.

Multiplying multiple term polynomials

You cannot use the FOIL method to multiply these polynomials. Instead, you have to multiply each term in one polynomial by each term in the other. You can do this by multiplying each term of one polynomial by the other polynomial. This can be tricky because it is easy to miss one term. When we do examples of this, it will become easier to understand how to solve them.

When multiplying polynomials, you may come across multiplying variables with exponents by variables with exponents. In this case, we use this exponent rule:
x^n\cdot x^m=x^(n+m)
For this rule, the base or variable must be the same. When multiplying variables with exponents, you add the exponents together.


Let’s see some examples to understand how to multiply polynomials.
First example (click here):
(2x-1)(5x-6)
We will use the FOIL method to solve this.
1.   Use FOIL identity
(2x-1)(5x-6)
2x\cdot 5x+2x\cdot -6+(-1)\cdot 5x+(-1)\cdot -6
2.   Multiply terms
10x^2-12x-5x+6
3.   Group like terms
10x^2-12x-5x+6
 (Luckily, everything was already grouped together)

4.   Add like terms
10x^2-17x+6

Next example (click here):
(2x^2+6)(2x^2-6)
Here, we can use another one of the identities for multiplying two term polynomials.
1.   Use (a+b)(a-b)=a^2-b^2
(2x^2+6)(2x^2-6)
(2x^2 )^2-6^2
2.   Simplify
4x^4-6^2
4x^4-36
Last example (click here):
(x^2+2x-1)(2x^2-3x+6)
1.   Multiply each term in one polynomial by the other polynomial
x^2 (2x^2-3x+6)+2x(2x^2-3x+6)-1(2x^2-3x+6)
2.   Distribute and multiply
2x^2\cdot x^2-3x\cdot x^2+6\cdot x^2+2x^2\cdot 2x-3x\cdot 2x+6\cdot 2x+2x^2\cdot -1-3x\cdot -1+6\cdot -1
2x^4-3x^3+6x^2+4x^3-6x^2+12x-2x^2+3x-6
3.   Group like terms
2x^4-3x^3+6x^2+4x^3-6x^2+12x-2x^2+3x-6
2x^4-3x^3+4x^3+6x^2-6x^2-2x^2+12x+3x-6
4.   Add like terms
2x^4+x^3+6x^2-6x^2-2x^2+12x+3x-6
2x^4+x^3-2x^2+12x+3x-6
2x^4+x^3-2x^2+15x-6

Multiplying polynomials looks intimidating, but as long as you keep your work neat and double check your work, it should be pretty easy. Practice will be one of the biggest things that will help you. The more you practice, the easier multiplying polynomials will be because you will get the hang and flow of how to multiply them. Check out Symbolab’s Practice for more help and practice.

Until next time,

Leah

46 comments:

  1. Thanks for sharing.I found a lot of interesting information here. A really good post, very thankful and hopeful that you will write many more posts like this one.
    https://notepad.software/
    vidmate
    https://filezilla.software/

    ReplyDelete
  2. You should know how to write a good business analyst resume! Take a close look to this guide!

    ReplyDelete
  3. For this rule, the base or variable must be the same. When multiplying variables with exponents, you add the exponents together. C1000-010 exam dumps

    ReplyDelete
  4. I was searching for something like this for quite a long time and at last I’ve found it on your blog. It was definitely interesting for all users i must want to write my paper for me appreciate your thoughts you have already shared though this post.

    ReplyDelete
  5. I like this website pretty much. Great info. Hi and thanks for the web blogs. Expert comptable Guadeloupe

    ReplyDelete
  6. Nice Post! The weakness of Verizon Verizon Swot Analysis is that it charges more money than its competitors for providing their service.

    ReplyDelete
  7. I am reading first time about mobile massage and from the first look I consider it as the professional would be providing tips for massage to people living in remote areas. Ben Barnes Shearling Jacket Well, you come up with exciting thing for the people looking for relaxed life.

    ReplyDelete
  8. Assignment help Online provides you best support on the assignment related to management and business and business operations. Online Assignment Help

    ReplyDelete
  9. Mathematics is very tuff subject if you can not unerstand when students need help in education there are many online websites which provides math assitance forhe weak students.

    ReplyDelete
  10. We do provide many facilities to the students who are said to be pursuing their academic courses in Melbourne. Along with our qualified Melbourne tutors, the online assignment writing service also includes pre-solved question papers, sample assignments and practice manuals for the required topic. We even let the students to choose up with the assignment help, which they are in need of under different courses and subjects.
    For further information & queries, Visit our website assignment help melbourne

    ReplyDelete
  11. thank you.
    คาสิโนออนไลน์ที่น่าเชื่อถือและมีความเป็นมืออาชีพที่สุดในตอนนี้
    โปรโมชั่นGclub ของทางทีมงานตอนนี้แจกฟรีโบนัส 50%
    เพียงแค่คุณสมัคร สล็อตออนไลน์ กับทางทีมงานของเราเพียงเท่านั้น
    ร่วมมาเป็นส่วนหนึ่งกับเว็บไซต์คาสิโนออนไลน์ของเราได้เลยค่ะ
    สมัครสล็อตออนไลน์ >>> Goldenslot
    สนใจร่วมสนุกกับ คาสิโนออนไลน์ คลิ๊กได้เลย
    มีทั้งคาสิโนออนไลน์ หวยออนไลน์ ฟุตบอลออนไลน์ สล็อตออนไลน์ และอื่นๆอีกมากมาย

    ReplyDelete
  12. We are prepared to deliver reliable and trusted Write My Research Papers services in all the outlined levels of study due to the many experts that we have in our company. Our College Research Paper is affordable and cheap as well for students who have very limited cash flows, and their budgets are usually constrained.

    ReplyDelete
  13. When students don’t have enough time to complete their assignments they search for online writes to write my assignment for me. In that case, they can get instant help from expert writers of Myassignmenthelp.com to when they request to write my assignment. The life of a student involves the dilemma of preparing multiple assignments at once like homework, dissertation, thesis paper, research paper and more. Well, you can be sure that your prayers have been heard, as MyAssignmenthelp.com is here to salvage your academic performance.

    ReplyDelete
  14. The dissertation can be influenced by many things, which one of them is the length of the work. Writing dissertation is the way to show your expertise on a certain subject, but it should maintain some courtesies in order to present them in front of a dissertation committee. The length factor could be a great impact while evaluating dissertations. So one should be careful about the length and have a fair idea of what be an average length of a dissertation. To get a great idea regarding the perfect length of a dissertation paper, click here and get assistance.

    ReplyDelete
  15. Your blog is very good and very informative. Your blog post is very useful. It is exceptionally accommodating for me I learn new information from your post. I truly love your blog post.Thank you for sharing this post with us keep it up.Students always asking us how to write an annotated bibliography in USA? What we suggest them is to hire assignment helper from 500+ writers online which were write your assignment with the help of best free plagiarism checker . For More Detail : Harvard Referencing generator

    ReplyDelete
  16. StudentsAssignmentHelp.com provides the best services of Do My Assignment Help. Get your Assignment Services at the best price and improve your grades. Our 3000+ Expert writers provide the best services of Assignment Writing for all College students. For more information contact here- +44-755-536-9184.or [email protected]

    ReplyDelete
  17. Translation Services Singapore is striving towards creating a great academic translation platform to the college and universities students so they can easily understand the subject matter. Our high experienced team of professional translators avails 24X7 for authentic translation help in desired languages.

    ReplyDelete
  18. Are you under the stress due to tight deadline and essay submission? Your search for finding the expert who can "write my essay online" ends here at EssayAssignmentHelp.com.au.
    Students come to us and say “I can pay for essay writer, but I need high-quality essay”. If you are one of those, we are here to help you out.
    Don’t lose your academic grades, just hire the best essay editors and proofreaders for your essay for both school and college level.

    ReplyDelete
  19. In a time when students are daily pressed for custom assignment writing service and multiple meeting multiple deadlines and keeping up with classes, the tempo to reflect on one’s own achievements and developments as a student and person, might be difficult to come by. Especially during those crucial times when students require and search for admissions essay help and ‘tips on college essays’ on the internet, it becomes strategically imperative to reevaluate one’s own personal development in an ordered way. If you need assignment help, just ask us to do my essay. Very often students fail to deliver essays that keep a fair level of balance between their personal and extra-curricular achievements and their academic development. Know more about information technology assignment help.

    ReplyDelete
  20. With our 360 IT Assignment Help services, you can quickly sort out all such problems. For your aid, we have even simplified our order processing steps. So now all our excellent assistive services are yours to avail without any complication.

    ReplyDelete
  21. A good blog always comes-up with new and exciting information and while reading I have feel that this blog is really have all those quality that qualify a blog to be a one write my essay

    ReplyDelete
  22. Are you looking to hire the best Custom Research Paper Services? It is tedious and overwhelming crafting Research Paper Assistance Services for learners, Custom Dissertation Writing Service can be basic complex with detailed instructions from the teacher.

    ReplyDelete
  23. Professional Online Thesis Writing Services, avail the best help for your Thesis Writing here at AssignmentStudio.

    ReplyDelete
  24. Are you looking to hire the best Custom Research Paper Services? It is tedious and overwhelming crafting Research Paper Assistance Services for learners, Custom Dissertation Writing Service can be basic complex with detailed instructions from the teacher.

    ReplyDelete
  25. At MyAssignmenthelp.com, we understand that attending a nursing course can be more taxing than it seems. You don’t just need to study and appear for tests. You also need to prepare a number of assignments and tasks, including nursing dissertations. And if you cannot spare enough time for these tasks, it won't be possible for you to pnurepare a remarkable paper without any kind of nursing dissertation help.
    We keep things very simple at MyAssignmenthelp.com. All our services that offer nursing dissertation help online are easy to avail. And most importantly, they cater to the specific needs of your dissertation. Just let us know about your requirements, and we will deliver the much-needed assistance accordingly.
    Philosophy dissertation help

    ReplyDelete
  26. I(Elizbath) express that All the understudy needs to do is to connect with us, feed us the necessities of the undertaking related to any academic field and we will ensure that the assignment work is adequate. Purchaser reliability is our primary need and there is 100% affirmation that our understudies will score best grades in the assignments gave by us To extra information addresses visit our site SPSS Help

    ReplyDelete
  27. Looking for essay help online ?. Want essay assignment help? Let’s have a look at our endeavors!MyAssignmenthelp AU have a range of professional writers ready to provide essay assignment help or essay help to the students presenting top quality essays, keeping in mind the instruction provided by their professors.

    ReplyDelete

  28. Harvard referencing is a note citation system to cite the academic papers or any important documents. This referencing generator tool is also known as the documentary style note. To include the process of referencing and citations in the academic paper is very important to increase the readability of the paper and it will eventually help students in scoring good grades. This Harvard citation generator tool has been designed to create the most accurate formatting and referencing style for your academic paper, that too within a matter of minutes. So all your confusion over Harvard citation and referencing style will be resolved when you select our online Harvard reference generator tool from Allessaywriter.com.

    ReplyDelete
  29. A debt of gratitude is in order for sharing this blog. An incredible data you shared through this blog. Keep it up and good luck for your future sites and posts. spss help

    ReplyDelete
  30. We know it becomes frustrating when we got stuck with an academic paper that seems impossible to solve. Well, we have the perfect solution for you. Just avail our academic paper writing service in three simple steps and submit an impeccably drafted paper within the instructed deadline. No matter how complex or uncommon the problem is, we have the necessary resources to deal with it easily.

    Writing help is one of the oldest running paper writing services on the internet that has been consistent in helping students with their academic needs. In fact, we have introduced a number of custom paper writing service Singapore that can solve your specific needs with perfection. So, place an order today and see a positive change in your academic performance.

    ReplyDelete
  31. Assignment Help Sydney offered by skilled and experienced writers of Assignment Studio

    ReplyDelete
  32. My assignment help was already offering the services at the lowest price in the market.
    Myassignmenthelp shines like a bright star.
    I've received so much referral credits that now I can order an assignment service for me without digging into my pocket money. This is why I love Myassignmenthelp review.
    Must Read Free education to student.

    ReplyDelete
  33. Amazing knowledge and I like to share this kind of information with my friends and hope they like it they why I do dissertation writing services

    ReplyDelete
  34. Essay writers Australia service by Australian assignment help. Do you need the premium quality essay writing help, then look no more search. We provide instant assignment help in Australia. We are offering amazing writing services at low price.

    ReplyDelete
  35. A decent blog consistently concocts new and energizing data and keeping in mind that perusing I have feel that this blog is truly have every one of those quality that qualify a blog to be a one. assignment helps

    ReplyDelete
  36. I will be interested in more similar topics. i see you got really very useful topics , i will be always checking your blog thanks Buy Instagram Followers

    ReplyDelete