### Multiplication of Polynomials

#### Review:

Watch Khan Academy's Video on using the FOIL method to multiply polynomials.

Khan Academy Multiplying Polynomials

- To multiply polynomials you use the _____ property.
- If solving for \begin{align*}3(9x+6)\end{align*}for example, you would distribute the __ unto the 9x and the 3 unto the __.
- Which of the following describes the action above? \begin{align*}(3\times9x)+(3\times6)\end{align*} OR \begin{align*}(3\times9x)\times(3\times6)\end{align*}

- When multiplying polynomials, you must use the distributive property...
- once
- twice
- multiple times (it depends on the specific polynomial)

- True or False? Binomials are the same thing as polynomials.

#### FOIL Method

FOIL stands for first, outer, inner, ____. To FOIL, first multiply the first term in each of the parentheses together. Then multiply the outer terms in each of the parentheses together. Next multiply the inner terms of the parentheses together. ____ the last/ending terms of each of the parentheses together. Finally, * add* each of the products together and combine ____ to get your final answer.

1) Find the product of \begin{align*}(x+6)(x+5)\end{align*} using the FOIL method. If you need help, click here.

2) FOIL \begin{align*}(2x+5)(x-3)\end{align*}.

3) FOIL \begin{align*}(4x+3)(2x^2+3x-5)\end{align*}. (See below for how to solve this problem.)

**Method:**

Although this problem may appear different because you are multiplying a binomial by a polynomial, you still use the distributive property. Unlike problem #1 where you were only distributing each number onto two terms, here you have to distribute some of the terms onto *three* other terms. This picture below demonstrates this distribution.

4) FOIL

- \begin{align*}-4s^2(3s^3+7s^2+11)\end{align*} Careful with the exponents!
- \begin{align*}(2g-5)(3g^3+9g^2+7g+12)\end{align*}