Multiplying Polynomials Worksheets
Free Multiplying Polynomials Worksheets with Complete Answer Keys
Free Multiplying Polynomials Worksheets with Answer Keys
Do you need a few Multiplying Polynomials Worksheets to give you or your students some extra practice with performing this important algebra skill?
This page includes a completely free library of printable multiplying polynomials worksheets that are available as printable PDF files. Every multiplying polynomials worksheet has several practice problems on the first page and a complete answer key on the second page.
You can download any of our multiplying polynomials worksheets by clicking on the blue text links in the library below. Once you click on any of the blue text links, a preview window will open where you can preview the practice problems and choose to either save the PDF file to your device or to print (the worksheets can be printed in color or in black-and-white).
This page also includes a short review section that recaps a few examples of how to perform multiplying polynomials in case you need some help with solving problems on any multiplying polynomials worksheet (you can also use the attached answer keys to check your answers as you go).
All of the free multiplying polynomials worksheets shared below are sample worksheets from the Mashup Math K-12 Infinite Worksheet Libraries available on the Mashup Math. | Quick Reference: How to Download/Print
Multiplying Polynomials Worksheets
Intermediate
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Advanced
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Multiplying Polynomials Worksheet Review
If you are having issues with solving problems on any multiplying polynomials worksheet shared in the library above, then we highly recommend that you read through this short review of how to multiply polynomials.
For starters, in order to learn how to multiply polynomials, it is imperative that you have a strong understanding of the distributive property, which allows you to multiply term by an expression by multiplying each term separately and the combining each resulting product together (and combining like terms when necessary) to create a new, equivalent expression.
By definition, if a, b, and c are real numbers, then the distributive property tells us that:
a(b+c) = ab + ac
So, for example, we could use the distributive property to expand 5(x+6) as follows:
5(x+6) = 5(x) + 5(6) = 5x + 30
As long as you understand the distributive property, you can apply the concept to solving problems on the multiplying polynomials worksheets and the multiplying polynomials by polynomials worksheets shared in the library above.
Figure 01: Multiplying Polynomials and the Distributive Property.
Now let’s extend this understanding of the distributive property to multiplying a monomial by a polynomial to solve the following problem:
4x²(3x² - 5x + 9)
We can multiply simply by using the distributive property by “distributing” the 4x² term and multiplying it by each term of the polynomial 3x² - 5x + 9 as follows:
4x²(3x² - 5x + 9) = 4x²(3x²) + 4x²(-5x) + 4x²(9) = 12x⁴ -20x³ + 36x²
And, since we can not combine any like terms to simply our result, we can conclude that:
4x²(3x² - 5x + 9) = 12x⁴ -20x³ + 36x²
Make sure that you are comfortable with solving these types of problems before moving onto multiplying polynomials by polynomials worksheet problems.
Figure 02: Multiplying Polynomials by Polynomials Worksheet Example
Now let’s take a look at an example problem that will resemble many of the problems that you will see of the multiplying polynomials worksheets above.
Consider the problem (7x-9)(3x² -6x +2).
We can find the product of these two polynomials by using the distributive property. However, in this case, we have to multiply each term from the first polynomial, (7x-9) by each term of the second polynomial, (3x² -6x +2), as follows:
7x(3x² -6x +2) + -9(3x² -6x +2)
Notice how we “split” the first polynomial into two monomials and then multiplied each one separately. Then we can distribute, combine like terms if possible, and find the final answer as follows:
7x(3x² -6x +2) = 21x³ - 42x² + 14x
-9(3x² -6x +2) = -27x² +54x - 18
Then we can find the sum of our two results as follows:
21x³ - 42x² + 14x + -27x² +54x - 18
= 21x³ -69x² +68x -18
So, we can conclude that our final answer is 21x³ -69x² +68x -18.
This process can be applied to solving a variety of algebra problems including problems on any multiplying polynomials worksheet shared on this page. Now that have review how to multiply polynomials, go ahead and try some of the practice worksheets above. The more that you practice, the easier solving these types of problems will be!
