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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.

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Presentation on theme: "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."— Presentation transcript:

1 factor using difference of squares.

2 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

3 Determine the pattern … = 1 2 = 2 2 = 3 2 = 4 2 = 5 2 = 6 2 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

4 Review: Multiply (x – 2)(x + 2) First terms: Outer terms: Inner terms: Last terms: Combine like terms. x 2 – 4 x-2 x +2 x 2 +2x -2x -4 This is called the difference of squares. x2x2 +2x -2x -4 Notice the middle terms eliminate each other!

5 Difference of Squares a 2 - b 2 = (a - b)(a + b) or a 2 - b 2 = (a + b)(a - b) The order does not matter!!

6 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!!!

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

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

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

10 Factor x 2 – y 2 1.(x + y)(x + y) 2.(x – y)(x + y) 3.(x + y)(x – y) 4.(x – y)(x – y) Remember, the order doesnt matter!

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

12 Factor 18c 2 + 8d 2 1.prime 2.2(9c 2 + 4d 2 ) 3.2(3c – 2d)(3c + 2d) 4.2(3c + 2d)(3c + 2d) You cannot factor using difference of squares because there is no subtraction!

13 Factor m 2 Rewrite the problem as 4m 2 – 64 so the subtraction is in the middle! 1.prime 2.(2m – 8)(2m + 8) 3.4(-16 + m 2 ) 4.4(m – 4)(m + 4)

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