Tuesday, July 1Tuesday, July 1Special FactoringSpecial Factoring

Difference of SquaresDifference of SquaresExample: Example: mm22 – 64 – 64

(m)2 – (8)2

(m + 8)(m – 8)

Example 2: 36x2 – 49y2

(6x)2 – (7y)2

(6x + 7y)(6x – 7y)

Example 3: 48a3 – 12a12a(4a2 – 1)12a((2a)2 – (1)2)12a(2a + 1)(2a – 1)

Example 4: 2x4 – 1622(x4 – 81)2((x2)2 – (9)2)2(x2 + 9)(x2 – 9)2(x2 + 9)((x)2 – (3)2)2(x2 + 9)(x + 3)(x –

3)

Now you try!Now you try!Example: 4yExample: 4y44 - 2500 - 2500

Example: 5xExample: 5x33 + 15x + 15x22 – 5x – 15 – 5x – 15

4(y2 + 25)(y + 5)(y – 5)

5(x + 1)(x – 1)(x + 3)

Sum of SquaresSum of Squares

General Formula: (x)2 + (y)2

PRIME!!! Cannot be factored

Difference of CubesDifference of CubesGeneral Formula: (a)3 – (b)3

(a – b)(a2 + ab + b2)Example: x3 – 27

(x)3 – (3)3

(x – 3)(x2 + 3x + (3)2)

(x – 3)(x2 + 3x + 9)

Sum of CubesSum of CubesGeneral Formula: (a)3 + (b)3

(a + b)(a2 – ab + b2)Example: c3d3 + 64

(cd)3 + (4)3

(cd + 4)((cd)2 – 4cd + (4)2)

(cd + 4)(c2d2 – 4cd + 16)

Perfect Square TrinomialsPerfect Square TrinomialsGeneral Formula: (a)2 + 2ab + (b)2

(a + b)2

General Formula: (a)2 – 2ab + (b)2

(a – b)2

Example: x2 – 12x + 36(x)2 – 2·x·6 + (6)2

(x – 6)(x – 6)

Factoring Review