## 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, 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: \(\left(x+3\right)\left(2{x}^{2}-5x+8\right).\)

### Solution

Distribute. | |

Multiply. | \(2{x}^{3}-5{x}^{2}+8x+6{x}^{2}-15x+24\) |

Combine like terms. | \(2{x}^{3}+{x}^{2}-7x+24\) |

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

## Example

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

### Solution

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

Multiply \(\left(2{x}^{2}-5x+8\right)\) by 3. | |

Multiply \(\left(2{x}^{2}-5x+8\right)\) by \(x\). | |

Add like terms. |