Teaching Notes 5.9: Multiplying Two Polynomials
Multiplying polynomials involves using the distributive property and simplifying similar terms.
Common errors include incorrectly applying the distributive property, incorrectly multiplying
monomials, and incorrectly combining similar terms.- Explain that when students multiply polynomials other than two binomials, they must apply
the distributive property, multiply monomials,and then combine similar terms. You may
mention that when multiplying two binomials, they may use the method described here or
use the steps of the acronym FOIL. Explain that FOIL is a mnemonic aid that summarizes how
to apply the distributive property when students multiply two binomials. - Review the information and example on the worksheet with your students. Because of the
complexity of the steps for multiplying polynomials, you might find it helpful to discuss
them in detail. Go over the example thoroughly and emphasize the steps of the distributive
property. Especially note that the second term of the first polynomial is−4 and each term of
the second polynomial is multiplied by−4.
EXTRA HELP:
Because several skills and concepts are applied when multiplying two polynomials, work carefully
to avoid careless mistakes. Always double-check your work.ANSWER KEY:
(1) 8 x^3 − 2 x^2 +x+ 2 (2)x^3 + 5 x^2 + 7 x+ 2 (3)x^3 − 4 x^2 + 4 x− 3
(4) 2 x^3 −x^2 − 7 x+ 20 (5) 3 x^3 − 14 x^2 + 17 x− 6 (6) 2 x^4 − 6 x^3 − 7 x^2 + 3 x+ 3
(7)x^4 − 3 x^3 + 3 x− 1 (8)x^5 − 7 x^4 + 2 x^3 − 4 x^2 + 28 x− 8 (9)x^4 + 7 x^3 − 9 x^2 +x
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(Challenge)Billy is incorrect. He multiplied each term of the second polynomial by 3 instead
of by−3. The correct answer isx^3 − 4 x^2 + 2 x+3.
------------------------------------------------------------------------------------------192 THE ALGEBRA TEACHER’S GUIDE