1. Lesson 5-3: Multiplying Polynomials Objectives Students will: Multiply any polynomials Multiply binomials using FOIL Square a binomial Multiply the sum & difference of two terms Cube a binomial

2. Day 1 Binomial X Binomial

3. Remember FOIL: Binomial X Binomial → F irst O uter I nner L ast or FOIL (3x + 2y)(5x + y)= Notice a 2 X 2 = 4 terms How many would a 3 X 4 have? 12 F O I L 15x 2 +3xy+ 2y 2 +10xy 15x 2 +13xy + 2y 2 Now CLT

4. Ex 2: (4x – 1)(2xy + 3x) Example 3: (x – 3) 2 Example 4: (x + 2)(x – 2) This is really (x- 3)(x-3)

5. Patterns Squaring Binomials (like Ex 3) (a + b) 2 = a 2 + 2ab + b 2 (a – b) 2 = a 2 – 2ab + b 2 (2x + 5) 2 = 4x 2 + 20x + 25 We get 10x for O and I so 20x Sum & Difference (like Ex 4) (a + b)(a – b) = a 2 – b 2 (F-L: OI cancel each other out) (3x – 2y)(3x + 2y)= 9x 2 - 4y 2

6. Day 1 Assignment 5-3 FOIL Worksheet

7. Day 2 Bigger than 2X2

8. Multiplying Polynomials Multiply: (a – 2b)(2a 2 – ab + b 2 )= 2a 3 -a 2 b+ab 2 -4a 2 b+2ab 2 -2b 3 then CLT 2a 3 -5a 2 b+3ab 2 -2b 3 Think of it as “multiple distribution” ►Each term from a polynomial times each term in the other 0r ►Use Geometric Box (good for larger than binomials) Notice a 2 X 3 =6 terms

9. Example 2: (Geo Method) ( 3a 2 - 2a + 4)(a 2 + 5a + 1) Wow the diagonals are like terms! Easy to combine!!

10. Ex 4: (x + y)(2x – y + 3)

11. Ex 5: (2x 2 -3x +2)(3x 3 -4x 2 +2x -1) Answer: 6x 5 -17x 4 + 22x 3 -16x 2 + 7x - 2

12. Cubing Binomials: Proof (a + b) 3 (a +b)(a+b) 2 (a+b)(a 2 + 2ab + b 2 ) (a+b)a 2 + (a+b)2ab + (a+b)b 2 a 3 +a 2 b +2a 2 b+2ab 2 +ab 2 +b 3 a 3 + 3a 2 b + 3ab 2 + b 3 Formula to Know: (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 (a – b) 3 = a 3 – 3a 2 b + 3ab 2 – b 3 → All + → +, -, +, - distribute (a+b) Combine Like Terms: CLT Similar proof for subtraction

13. Try 6 (2x – 3y) 3 Answer: 8x 3 -36x 2 y + 54xy 2 - 27y 3

14. Assignment