Objective The student will be able to: factor using difference of squares.

Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms 1. GCF 2 or more 2. Difference of Squares 2

Determine the pattern 1 4 9 16 25 36 … = 12 = 22 = 32 = 42 = 52 = 62 These are perfect squares! You should be able to list the first 15 perfect squares in 30 seconds… Perfect squares 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Review: Multiply (x – 2)(x + 2) Notice the middle terms eliminate each other! x2 First terms: Outer terms: Inner terms: Last terms: Combine like terms. x2 – 4 x -2 +2 +2x -2x x2 -2x -4 +2x -4 This is called the difference of squares.

The order does not matter!! Difference of Squares a2 - b2 = (a - b)(a + b) or a2 - b2 = (a + b)(a - b) The order does not matter!!

4 Steps for factoring Difference of Squares 1. Are there only 2 terms? 2. Is the first term a perfect square? 3. Is the last term a perfect square? 4. Is there subtraction (difference) in the problem? If all of these are true, you can factor using this method!!!

When factoring, use your factoring table. 1. Factor x2 - 25 When factoring, use your factoring table. Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? Write your answer! No x2 – 25 Yes Yes Yes Yes ( )( ) x + 5 x - 5

When factoring, use your factoring table. 2. Factor 16x2 - 9 When factoring, use your factoring table. Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? Write your answer! No 16x2 – 9 Yes Yes Yes Yes (4x )(4x ) + 3 - 3

When factoring, use your factoring table. 3. Factor 81a2 – 49b2 When factoring, use your factoring table. Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? Write your answer! No 81a2 – 49b2 Yes Yes Yes Yes (9a )(9a ) + 7b - 7b

Factor x2 – y2 (x + y)(x + y) (x – y)(x + y) (x + y)(x – y) Remember, the order doesn’t matter!

When factoring, use your factoring table. 4. Factor 75x2 – 12 When factoring, use your factoring table. Do you have a GCF? 3(25x2 – 4) Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? Write your answer! Yes! GCF = 3 Yes 3(25x2 – 4) Yes Yes Yes 3(5x )(5x ) + 2 - 2

Factor 18c2 + 8d2 prime 2(9c2 + 4d2) 2(3c – 2d)(3c + 2d) You cannot factor using difference of squares because there is no subtraction!

Rewrite the problem as 4m2 – 64 so the subtraction is in the middle! Factor -64 + 4m2 prime (2m – 8)(2m + 8) 4(-16 + m2) 4(m – 4)(m + 4) Rewrite the problem as 4m2 – 64 so the subtraction is in the middle!