1. Multiplying Polynomials Be able to use different methods to multiply two polynomials.

2. FHSPolynomials2 Multiplying Polynomials To multiply polynomials together each term of the first polynomial must be multiplied by each term of the second polynomial. There are several methods for multiplying polynomials. The three methods we will be using are the box method, using the memory device FOIL, and using the distributive property.

3. FHSPolynomials3 The Box Method The simplest method for multiplying polynomials is to use a box or a chart to fill in. Here is an example:

4. FHSPolynomials4 How does FOIL work? Look at the example below to show FOIL at work: F = multiply the first term in each binomial O = multiply the two outside terms together I = multiply the two inside terms together L = multiply the last term in each binomial (x + 6)(2x +3) · + · + · + · = 2x 2 + 3x + 12x + 18 = 2x 2 + 15x + 18 x 2x2x 6 3 2x2x 6 3 x

5. FHSPolynomials5 The Distributive Method The third method is to use the distributive property to multiply each term of the first polynomial by each term of the second polynomial. You must use this method or the box method if you are multiplying polynomials that are not binomials.

6. FHSPolynomials6 Let’s Practice 1. (y – 5)(y – 1) = y 2 – y – 5y + 5 = y 2 – 6y + 5 2. (3xy + 4)(4xy – 5) = 12x 2 y 2 – 15xy + 16xy – 20 12x 2 y 2 + xy – 20 3. (5 – x)(5 + x) = 25 + 5x – 5x – x 2 = 25 – x 2 4. (y + 2) 2 = (y + 2)(y + 2) = y 2 + 2y + 2y +4 = y 2 + 4y + 4