Objective: I will be able to: use patterns to multiply special binomials

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

1. Multiply: (x + 4)2 You can multiply this by rewriting this as (x + 4)(x + 4) OR You can use the Square of a Binomial Pattern: (a + b)2 = a2 + 2ab + b2

Notice you have two of the same answer 1. Multiply (x + 4)(x + 4) Notice you have two of the same answer x2 First terms: Outer terms: Inner terms: Last terms: Combine like terms. x2 +8x + 16 x +4 +4x +4x x2 +4x +16 +4x +16

1. Multiply: (x + 4)2 using (a + b)2 = a2 + 2ab + b2 That’s why the 2 is in the formula! 1. Multiply: (x + 4)2 using (a + b)2 = a2 + 2ab + b2 a is the first term, b is the second term (x + 4)2 a = x and b = 4 Plug into the formula a2 + 2ab + b2 (x)2 + 2(x)(4) + (4)2 Simplify. x2 + 8x+ 16 This is the same answer

Plug into the formula a2 + 2ab + b2 Guided Practice Multiply: (3x + 2y)2 using Square of a Binomial Pattern (3x + 2y)2 a = 3x and b = 2y Plug into the formula a2 + 2ab + b2 (3x)2 + 2(3x)(2y) + (2y)2 Simplify 9x2 + 12xy +4y2

Multiply: (x – 5)2 using (a – b)2 = a2 – 2ab + b2 Multiply: (x – 5)2 using (a – b)2 = a2 – 2ab + b2 *Everything is the same except the signs (x)2 – 2(x)(5) + (5)2 x2 – 10x + 25 4. Multiply: (4x – y)2 (4x)2 – 2(4x)(y) + (y)2 16x2 – 8xy + y2

Notice the middle terms eliminate each other! 5. Multiply (x – 3)(x + 3) Notice the middle terms eliminate each other! x2 First terms: Outer terms: Inner terms: Last terms: Combine like terms. x2 – 9 x -3 +3 +3x -3x x2 -3x -9 +3x -9 This is called the difference of squares.

Continued… Multiply (x – 3)(x + 3) using (a – b)(a + b) = a2 – b2 *You can only use this rule when the binomials are exactly the same except for the sign. (x – 3)(x + 3) a = x and b = 3 (x)2 – (3)2 x2 – 9

6. Multiply: (y – 2)(y + 2) (y)2 – (2)2 y2 – 4 7. Multiply: (5a + 6b)(5a – 6b) (5a)2 – (6b)2 25a2 – 36b2

Independent Practice Multiply (2a + 3)2 4a2 + 36a + 9 4a2 + 12a + 9

Multiply (x – y)2 x2 + 2xy + y2 x2 – 2xy + y2 x2 + y2 x2 – y2

Multiply (4m – 3n)(4m + 3n) 16m2 – 9n2 16m2 + 9n2 16m2 – 24mn - 9n2