How to Multiply Polynomials With Distributive Properties

Learn to multiply polynomials with the distributive property.

The word poly means many. It is the prefix of the word polynomial which means many terms. In math class, a polynomial is an equation composed of many terms which may include variables or exponents. The terms of a polynomial are combined using addition, subtraction and multiplication; however, polynomials are not combined using division. Using the distributive property of multiplication, in which multiplication distributes over addition, it is easy to combine and simplify polynomials. For example, the distributive property states that 7(4+3) produces the same answer as 7x4+7x3.

Things You'll Need

• Blank sheet of paper
• Pencil
• Calculator

Instructions

1. Create an equation on a clean sheet of paper, using a pencil.

2. Write out a polynomial equation using only letters. Using letters allows you to better understand polynomials and the distributive property before incorporating numbers. Write down the equation (a+b+c) (d+e+f). This equation is a polynomial because it incorporates multiple terms.

3. Distribute each term in the first polynomial across the second polynomial, using the distributive property. For example, a(d+e+f) + b(d+e+f) + c(d+e+f). Use the distributive property until each term of the first polynomial is multiplied by every term in the second polynomial. For example, (a*d)+(a*e)+(a*f)+(b*d)+(b*e)+(b*f)+(c*d)+(c*e)+(c*f). Use every combination of each term.

4. Write in numbers in place of the letters, using the same equation. Write (7+11+4) (8+5+3).

5. Distribute 7, followed by 11 and then 4 across the second polynomial. For example, 7(8+5+3) + 11(8+5+3) + 4(8+5+3). Next, distribute over the second polynomial so (7*8)+(7*5)+(7*3)+(11*8)+(11*5)+(11*3)+(4*8)+(4*5)+(4*3).

6. Combine the terms. Use a calculator to check your math. You should end up with 56+35+21+88+55+33+32+20+12. Combine the terms one final time. Your final answer is 352.

Tips & Warnings

• When working with variables, combine like terms and simplify the problem as far as you can. It is okay if your answer contains variables.

• Multiplying polynomials with the distributive property takes practice. Continue to practice using this method until you are comfortable with the process before moving on to more complicated polynomials.

References

• Math is Fun: Polynomials
• Purplemath: Basic Number Properties: Associative, Commutative, and Distributive
• AAA Math: Multiplication Properties
• Spark Notes: Multiplication of Polynomials
• West Texas A&M University: Beginning Algebra Tutorial 28: Multiplying Polynomials