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Multiplying a Trinomial By a Binomial

Multiplying a Trinomial by a Binomial

We have multiplied monomials by monomials, monomials by polynomials, and binomials by binomials. Now we’re ready to multiply a trinomial by a binomial. Remember, FOIL will not work in this case, but we can use either the Distributive Property or the Vertical Method. We first look at an example using the Distributive Property.

Example

Multiply using the Distributive Property: \(\left(b+3\right)\left(2{b}^{2}-5b+8\right).\)

Solution

 The product of a binomial, b plus 3, and a trinomial, 2 b squared minus 5 b plus 8. Two arrows extend from the trinomial, terminating at b and 3 in the binomial.
Distribute.The sum of two products, the product of b and 2 b squared minus 5 b plus 8, and the product of 3 and 2 b squared minus 5 b plus 8.
Multiply.2 b cubed minus 5 b squared plus 8 b plus 6 b squared minus 15 b plus 24.
Combine like terms.2 b cubed plus b squared minus 7 b plus 24.

Now let’s do this same multiplication using the Vertical Method.

Example

Multiply using the Vertical Method: \(\left(b+3\right)\left(2{b}^{2}-5b+8\right).\)

Solution

It is easier to put the polynomial with fewer terms on the bottom because we get fewer partial products this way.

Multiply (2b2 − 5b + 8) by 3..
 .
Multiply (2b2 − 5b + 8) by b..
Add like terms. 

We have now seen two methods you can use to multiply a trinomial by a binomial. After you practice each method, you’ll probably find you prefer one way over the other. We list both methods are listed here, for easy reference.

Multiplying a Trinomial by a Binomial

To multiply a trinomial by a binomial, use the:

  • Distributive Property
  • Vertical Method

Optional Videos:

Access these online resources for additional instruction and practice with multiplying polynomials:

Multiplying Exponents 1

Multiplying Exponents 2

Multiplying Exponents 3

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