# 1 Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use Binomial Products Stage 6 - Year 11 Mathematic (Preliminary)

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1 Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use Binomial Products Stage 6 - Year 11 Mathematic (Preliminary)

2 Binomial Products FOIL Method (a + b)(x + y) = Firsts, Outers, Inners, Lasts.

3 Binomial Products FOIL Method (a + b)(x + y) = Firsts, Outers, Inners, Lasts.   ax   

4 Binomial Products FOIL Method (a + b)(x + y) = Firsts, Outers, Inners, Lasts.  ax+ ay  

5 Binomial Products FOIL Method (a + b)(x + y) = Firsts, Outers, Inners, Lasts. ax+ ay   + bx 

6 Binomial Products FOIL Method (a + b)(x + y) = Firsts, Outers, Inners, Lasts.  ax+ ay   + bx+ by

7 Binomial Products FOIL Method (a + b)(x + y) = Firsts, Outers, Inners, Lasts. or Distributive Method (a + b)(x + y) = ax+ ay+ bx+ by

8 Binomial Products FOIL Method (a + b)(x + y) = Firsts, Outers, Inners, Lasts. or Distributive Method (a + b)(x + y) =  ax+ ay  + bx+ by a(x + y)

9 Binomial Products FOIL Method (a + b)(x + y) = Firsts, Outers, Inners, Lasts. or Distributive Method (a + b)(x + y) = ax+ ay+ bx+ by + b(x + y)a(x + y) 

10 Binomial Products FOIL Method (a + b)(x + y) = Firsts, Outers, Inners, Lasts. or Distributive Method (a + b)(x + y) = = ax + ay + bx + by ax+ ay+ bx+ by + b(x + y)a(x + y)

11 Binomial Products Examples of Distributive Law (2x + 3)(3x + 2) =2x(3x + 2)+ 3(3x + 2) = 6x 2 + 4x+ 9x + 6 = 6x 2 + 13x + 6

12 Binomial Products Examples of Distributive Law (x - 5)(2x - 3) = x(2x - 3) - 5(2x - 3) = 2x 2 - 3x - 10x + 15  Common Mistake = 2x 2 - 13x + 15

13 Binomial Products Related Products (a + b)(x + y + z) = ax + ay + az + bx + by + bz (2x +3)(x + y - 2) = = 2x 2 + 2xy - 4x + 3x + 3y - 6 = 2x 2 + 2xy - x + 3y - 6 = 2x(x + y - 2)+ 3(x + y - 2) Example

14 Binomial Products Special Products (a + b) 2 =a 2 + 2ab + b 2 Proof (a + b) 2 = (a + b)(a + b) = a(a + b) + b(a + b) = a 2 + ab+ ab + b 2 = a 2 + 2ab + b 2

15 Binomial Products Special Products (a + b) 2 =a 2 + 2ab + b 2 Example (2x + 3) 2 = (2x) 2 + 2 x 2x x 3 + 3 2 = 4x 2 + 12x + 9 aa bb

16 Binomial Products Special Products (a - b) 2 =a 2 - 2ab + b 2 Proof (a - b) 2 = (a - b)(a - b) = a(a - b) - b(a + b) = a 2 - ab- ab + b 2 = a 2 - 2ab + b 2

17 Binomial Products Special Products (a - b) 2 =a 2 - 2ab + b 2 Example (3x - 2) 2 = (3x) 2 - 2 x 3x x 2 + 2 2 = 9x 2 - 12x + 4 aa bb

18 Binomial Products Special Products (a + b)(a -b) =a 2 - b 2 Proof (a + b)(a - b) = = a(a - b) + b(a - b) = a 2 - ab + ab - b 2 = a 2 - b 2

19 Binomial Products Special Products (a + b)(a -b) =a 2 - b 2 Example (2x + 3y)(2x - 3y) = = 4x 2 - 9y 2 aa bb (2x) 2 - (3y) 2 aa bb

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