1. 8.7 Multiplying Polynomials

2. Multiplying a Binomial by a Binomial A binomial is a polynomial with two terms. To multiply a binomial by a binomial, you will use a method called “FOIL.” This process is called “FOIL” because you work the problem in this order: First Outer Inner Last

3. Multiplying a Binomial by a Binomial Example:(x + 2)(x + 3) Multiply the first terms in each binomial. Multiply the two outer terms in each binomial. Multiply the two inner terms in each binomial. Multiply the two last terms in each binomial. Simplify. ([x] + 2)([x] + 3) = x 2 ([x] + 2)(x + [3]) = x 2 (x + [2])([x] + 3) = x 2 + 3x (x + [2])(x + [3]) = x 2 + 3x + 2x = x 2 + 5x + 6 + 3x + 2x + 6

4. Multiplying a Binomial by a Binomial Example: (x + 3)(x –1) = (x + 1)(x + -1) Multiply the first terms in each binomial. Multiply the two outer terms in each binomial. Multiply the two inner terms in each binomial. Multiply the two last terms in each binomial. Simplify. ([x] + 3)([x] + -1) ([x] + 3)(x + [-1]) (x + [3])([x] + -1) (x + [3])(x + [-1]) = x 2 = x 2 – x = x 2 – x + 3x = x 2 + 2x – 3 – x + 3x – 3

5. Multiplying a Binomial by a Binomial Example:(2x + 1)(3x – 2) = (2x + 1)(3x + -2) Multiply the first terms in each binomial. Multiply the two outer terms in each binomial. Multiply the two inner terms in each binomial. Multiply the two last terms in each binomial. Simplify. ([2x] + 1)(3x + [-2]) (2x + [1])([3x] + -2) (2x + [1])(3x + [-2]) = 6x 2 = 6x 2 – 4x = 6x 2 – 4x + 3x = 6x 2 – x – 2 – 4x + 3x – 2 ([2x] + 1)([3x] + -2)

6. Multiplying a Binomial by a Trinomial Multiply each term in the first polynomial with each in the second polynomial. Multiply by 2 to each term in the second polynomial. Simplify. = x(x 2 + 2x + 1) = x 3 + 2x 2 + x = 2(x 2 + 2x + 1) = 2x 2 + 4x + 2 + 2x 2 + 4x + 2= x 3 + 2x 2 + x = x 3 + 4x 2 + 5x + 2 Example:(x + 2)(x 2 + 2x + 1) Analyze how you would multiply a binomial by a trinomial. A binomial has two terms, and a trinomial has three terms.