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Lesson 5-3: Multiplying Polynomials

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. Day 1. Binomial X Binomial. Binomial X Binomial → F irst O uter I nner L ast or FOIL.

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Lesson 5-3: Multiplying Polynomials

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  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. Binomial X Binomial → First Outer Inner Last or FOIL O Remember FOIL: F (3x + 2y)(5x + y)= 15x2 +3xy +10xy + 2y2 Now CLT I L 15x2 +13xy + 2y2 Notice a 2 X 2 = 4 terms How many would a 3 X 4 have? 12

  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 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2 (2x + 5)2= 4x2+ 20x + 25 We get 10x for O and I so 20x Sum & Difference (like Ex 4) (a + b)(a – b) = a2 – b2 (F-L: OI cancel each other out) (3x – 2y)(3x + 2y)= 9x2 - 4y2

  6. Day 1 Assignment 5-3 FOIL Worksheet

  7. Day 2 Bigger than 2X2

  8. Multiplying Polynomials Multiply: (a – 2b)(2a2 – ab + b2)= 2a3-a2b+ab2-4a2b+2ab2-2b3 then CLT 2a3-5a2b+3ab2-2b3 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. Wow the diagonals are like terms! Easy to combine!! Example 2: (Geo Method)( 3a2 - 2a + 4)(a2 + 5a + 1)

  10. (x + y)(2x – y + 3) • Ex 4:

  11. Ex 5: (2x2 -3x +2)(3x3-4x2+2x -1) Answer: 6x5 -17x4 + 22x3 -16x2 + 7x - 2

  12. Cubing Binomials: Proof (a + b)3 (a +b)(a+b)2 (a+b)(a2 + 2ab + b2) (a+b)a2 + (a+b)2ab + (a+b)b2 a3+a2b +2a2b+2ab2+ab2+b3 a3 + 3a2b + 3ab2 + b3 Formula to Know: (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a – b)3 = a3 – 3a2b + 3ab2 – b3 distribute (a+b) Combine Like Terms: CLT Similar proof for subtraction → All + → +, -, +, -

  13. Try 6 (2x – 3y)3 Answer: 8x3 -36x2y + 54xy2 - 27y3

  14. Assignment

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