This pdf includes the following topics:- Factoring Chart Determine the pattern Difference of Squares 4 Steps for factoring Difference of Squares
1. Notes 8.5 Factoring 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 = 12 These are perfect squares! 4 = 22 You should be able to list 9 = 32 the first 15 perfect 16 = 42 squares in 30 seconds… 25 = 52 Perfect squares 36 = 62 1, 4, 9, 16, 25, 36, 49, 64, 81, … 100, 121, 144, 169, 196, 225
4. Review: Multiply (x – 2)(x + 2) Notice the First terms: x2 middle terms eliminate x -2 Outer terms: +2x each other! Inner terms: -2x Last terms: -4 x x2 -2x Combine like terms. x2 – 4 +2 +2x -4 This is called the difference of squares.
5. Difference of Squares 2 2 a - b = (a - b)(a + b) or 2 2 a - b = (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 x2 - 25 When factoring, use your factoring table. Do you have a GCF? No Are the Difference of Squares steps true? Two terms? Yes x2 – 25 1st term a perfect square? Yes 2nd term a perfect square? Yes Subtraction? Yes ( x + 5 )(x - 5 ) Write your answer!
8. 2. Factor 16x2 - 9 When factoring, use your factoring table. Do you have a GCF? No Are the Difference of Squares steps true? Two terms? Yes 16x2 – 9 1st term a perfect square? Yes 2nd term a perfect square? Yes Subtraction? Yes (4x + 3 )(4x - 3 ) Write your answer!
9. 3. Factor 81a2 – 49b2 When factoring, use your factoring table. Do you have a GCF? No Are the Difference of Squares steps true? Two terms? Yes 81a2 – 49b2 1st term a perfect square? Yes 2nd term a perfect square? Yes Subtraction? Yes (9a + 7b)(9a - 7b) Write your answer!
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 doesn’t matter!
11. 4. Factor 75x2 – 12 When factoring, use your factoring table. Do you have a GCF? Yes! GCF = 3 3(25x2 – 4) Are the Difference of Squares steps true? Two terms? Yes 3(25x2 – 4) 1st term a perfect square? Yes 2nd term a perfect square? Yes Subtraction? Yes Write your answer! 3(5x + 2 )(5x - 2 )
12. Factor 18c 2 + 8d 2 1. prime 2. 2(9c2 + 4d2) 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 -64 + 4m2 1. prime 2. (2m – 8)(2m + 8) 3. 4(-16 + m2) 4. 4(m – 4)(m + 4) Rewrite the problem as 4m2 – 64 so the subtraction is in the middle!
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