Overview
On this page, we review how to multiply polynomials, by expanding and collecting like terms.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Multiply a polynomial by a monomial.
- Multiply a two binomials, using the “FOIL” mnemonic.
- Multiply two arbitrary polynomials.
- Multiply three polynomials, especially one monomial and two binomials.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Recognize the following special products of binomials and expand them quickly using the memorized formulas:
- sum and difference: \((a+b)(a-b)=a^2-b^2\)
- perfect square: \((a+b)^2=a^2+2ab+b^2\)
To prepare for class
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Watch the following video (by Tyler Wallace) which shows how to multiply a polynomial by just one term/monomial:
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Watch the following video (by Tyler Wallace) which shows how to multiply two binomials, using the “FOIL” mnemonic:
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Watch the following video (by Tyler Wallace) which shows how to multiply two general polynomials (using trionomials as examples):
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Watch the following video (by Tyler Wallace) which shows how to multiply three factors together, using the frequently occurring example of a monomial and two binomials:
After class
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Watch the following videos (by Tyler Wallace) which review two important special products which should never be expanded by hand but rather done more quickly using their memorized formulas: sum and difference (giving a difference of squares), and the perfect square of a binomial:
