Mathematics » Polynomials II » Multiply Polynomials

# 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  Distribute.  Multiply.  Combine like terms.  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: