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Before you get started, take this readiness quiz.
In Distributive Property you learned to use the Distributive Property to simplify expressions such as You multiplied both terms in the parentheses, by to get With this chapter's new vocabulary, you can say you were multiplying a binomial, by a monomial, Multiplying a binomial by a monomial is nothing new for you!
Multiplying a monomial by a trinomial works in much the same way.
Now we will have the monomial as the second factor.
Just like there are different ways to represent multiplication of numbers, there are several methods that can be used to multiply a binomial times a binomial.
We will start by using the Distributive Property . Look again at [link] .
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| We distributed the to get |
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What if we have
instead of
?
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| Distribute . |
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| Distribute again. | |
| Combine like terms. |
Notice that before combining like terms, we had four terms. We multiplied the two terms of the first binomial by the two terms of the second binomial—four multiplications.
Be careful to distinguish between a sum and a product.
Now we'll see how to multiply binomials where the variable has a coefficient .
Multiply:
| Distribute. . |
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| Distribute again. | |
| Simplify. |
In the previous examples, the binomials were sums. When there are differences, we pay special attention to make sure the signs of the product are correct.
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