Benjamin Franklin K-8 Center, Algebra I E.O.C.
Algebra & Math Education
Rewriting
rational expressions
Watch and complete your notes on the videos below.
Afterwards, read about Rewriting Rational Expressions. Then, test your knowledge!
Multiplying Polynomials
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To multiply two polynomials:
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multiply each term in one polynomial by each term in the other polynomial
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add those answers together, and simplify if needed
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Let us look at the simplest cases first.
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1 term × 1 term (monomial times monomial)
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To multiply one term by another term, first multiply the constants, then multiply each variable together and combine the result, like this (press play):
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(Note: I used "·" to mean multiply. In Algebra we don't like to use "×" because it looks too much like the letter "x")
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1 term × 2 terms (monomial times binomial)
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Multiply the single term by each of the two terms, like this:
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2 term × 1 terms (binomial times monomial)
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Multiply each of the two terms by the single term, like this:
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(That was a bit faster because you can use mental math before writing it down.)
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2 terms × 2 terms (binomial times binomial)
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Each of the two terms in the first binomial ...
... is multiplied by ...
... each of the two terms in the second binomial
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That is 4 different multiplications ... Why?
It is the same when we multiply binomials!
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Instead of Alice and Betty, let's just use a and b, and Charles and David can be c and d:
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We can multiply them in any order so long as each of the first two terms gets multiplied by each of the second two terms.
But there is a handy way to help us remember to multiply each term called "FOIL".
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It stands for "Firsts, Outers, Inners, Lasts":
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So you multiply the "Firsts" (the first terms of both polynomials), then the "Outers", etc.
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Let us try this on a more complicated example:
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2 terms × 3 terms (binomial times trinomial)
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"FOIL" won't work here, because there are more terms now. But just remember:
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Multiply each term in the first polynomial by each term in the second polynomial.
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Like Terms
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And always remember to add Like Terms:
