1. Algebra 10.2 Multiplying Polynomials

2. Consider a rectangular house It is 12 feet wide by 18 feet long OK...... it’s a small house....... 12 18

3. 12 18 What is the area of this small house? 12 x 18 216 It is 216 square feet.

4. 12 18 Let’s add interior walls to the house to make 4 rooms 108 2

5. 12 18 What is the square footage of each room? 108 2 10080 1620 Does it still add up to 216 ? 100 80 20 16 216 YES

6. 12 18 So the total product is equal to the sum of the smaller products. 108 2 10080 1620 100 80 20 16 216 = 12 x 18 216

7. ….and we can multiply the dimensions horizontally like this…. (10 + 8) (10 + 2) 100+ 20+80+16 = 216 12 18 108 2 10080 1620

8. x + 2 x + 8 Let’s do something “crazy” and x8 x 2 x²8x 162x say that 10 = x.

9. ….and we can multiply the dimensions horizontally like this…. (x + 8) ( x + 2) x²+ 2x+8x+16 = 216 Put the 10 back for x and check x + 2 x + 8 x8 x 2 x²8x 162x = x² + 10x + 16 = (10)² + 10(10) + 16

10. Multiplying Polynomials When multiplying polynomials, you use the distributive property. Each term in one polynomial gets multiplied by each term in the other polynomial. When a binomial is multiplied by another binomial, we refer to the pattern as “FOIL”

11. FOIL Stands for: (x + 8) ( x + 2) First x² + 2x + 8x + 16 = x² + 10x + 16 OutsideInsideLast

12. Try these (x + 7) (x – 3) (3x + 4)(x – 5) (2x – 5)(x – 3) (x + 3)(x – 3) x²+ 4x - 21 3x²- 11x - 20 2x²- 11x + 15 x²- 9

13. It works the same for multiplying binomials by other polynomials. (3x + 2)(x² – 5x + 3) 3x³- 15x² + 9x+2x²- 10x + 6 3x³- 13x²- x + 6 When you multiply a 2 by 3 you get 2 x 3 = 6 terms Then combine like terms

14. Homework pg. 587 # 19 - 47 odd, 54-55, 62-73