8-4 Special Products of Polynomials Goal: Use special product patterns for the product of a sum and a difference and for the square of a binomial. Eligible Content: A1.1.1.5.1

Try These Problems (x + 6) (x – 6) x2 – 6x + 6x – 36 x2 – 36

Special Product Patterns Sum and Difference Pattern (a + b)(a – b) Square of a Binomial Pattern (a + b)2 (a – b)2 a2 – b2 = a2 + 2ab + b2 = = a2 – 2ab + b2

Three ways to do these problems Remember the pattern and use it! Use FOIL Use the Box Method

Examples of Sum and Difference (x + 2)(x – 2) (x + 8)(x – 8) (2y – 3)(2y + 3) x2 – 4 x2 – 64 4y2 – 9

Examples of Square of a Binomial (3d + 1)2 (5x – 2)2 (2y – 1)2 x2 +6x + 9 9d2 + 6d+ 1 25x2 – 20x + 4 4y2 – 4y + 1

Find (3x + 2)2. A. 9x2 + 4 B. 9x2 + 6x + 4 C. 9x + 4 D. 9x2 + 12x + 4

Find (2m – 3)2. A. 4m2 + 9 B. 4m2 – 9 C. 4m2 – 6m + 9 D. 4m2 – 12m + 9

Find (3y + 2)(3y – 2). A. 9y2 + 4 B. 6y2 – 4 C. 6y2 + 4 D. 9y2 – 4

Practice Page 488 #1-6

Homework Page 489 #12-36 even