### Learning Outcomes

- Multiply 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, the FOIL method 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: [latex]\left(x+3\right)\left(2{x}^{2}-5x+8\right)[/latex]

Solution

Distribute. | [latex]x\color{red}{(2x^2-5x+8)}+3\color{red}{(2x^2-5x+8)}[/latex] |

Multiply. | [latex]2{x}^{3}-5{x}^{2}+8x+6{x}^{2}-15x+24[/latex] |

Combine like terms. | [latex]2{x}^{3}+{x}^{2}-7x+24[/latex] |

### try it

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

### example

Multiply using the Vertical Method: [latex]\left(x+3\right)\left(2{x}^{2}-5x+8\right)[/latex]

Show Solution

### try it

Watch the following video to see more examples of multiplying polynomials.