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# Factoring Special Products in Difference of Squares

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### Factoring Special Products in Difference of Squares

1. 1. Problem 1 9x2-4
2. 2. Problem 1 9x2 - 4 3x(3x) 2(2)Both of these can be squared so I will show you whatthey are squared by under them. To make our problemwe will try to fit the formula a2 + b2 = (a + b)(a-b). Sincethe first one is a2 (9x2), a is 3x, using this way ofthinking, I would say that b is 2. Our answer is on thenext page.
3. 3. Problem 1 9x2 – 4 = (3x + 2)(3x – 2)
4. 4. Example Problems a2 – 81 36m2 – 25 4x2 – y2 a2 + 64 Remember that both must be PERFECT squares.
5. 5. Example Problems a2 – 81 (a + 9)(a – 9) 36m2 – 25 (6m + 5)(6m – 9) 4x2 – y2 (2x + y)(2x – y) a2 + 64 This cannot be factored since this method doesn’t work with addition problems, only subtraction.
6. 6. Mini Lesson If you feel you are just doing the problems blindly, check them with F.O.I.L. and you will find that two of the numbers cancel out together.
7. 7. Problem 2 2a2 – 200
8. 8. Problem 2 2a2 – 200To make this problem work so that we have squareswe will have to divide it by 2. a2 – 100Now we can solve that to get (a + 10)(a – 10). We addthe 2 back by placing it next to the problem formultiplication, making our final answer look like theslide on the next page.
9. 9. Problem 2 2a2 – 200 = 2(a + 10)(a – 10)
10. 10. Problem 3 -4c2 + 36
11. 11. Problem 3 -4c2 + 36To make this work we will remember what we did inthe last problem and divide the problem by -4, makingit c2 - 9. Solving this the normal way we will get(c + 3)(c-3) which will change to be -4(c + 3)(c-3).
12. 12. Problem 3 -4c2 + 36 = -4(c + 3)(c-3)
13. 13. Formula a2 + 2ab + b2 = (a + b)(a + b) or (a + b)2
14. 14. Problem 4 25x2+ 10x + 1
15. 15. Problem 4 25x2+ 10x + 1We will answer this using the formula on slide 13.a2 + 2ab + b2 = (a + b)(a + b) or (a + b)225x2+ 10x + 1We will first get the square root the 25x2 (5x) and placeit in the ‘a’ place of the formula. Then we will get thesquare root of 1 (1) and place it in the ‘b’ place of theformula. The answer will be on the next slide.
16. 16. Problem 4 25x2+ 10x + 1 = (5x + 1)2
17. 17. Problem 5 144y2 - 120y + 25
18. 18. Problem 5 144y2 - 120y + 25We need to find a way to accommodate the negativesign in the middle so just blindly using our formula toget (12y + 5)(12y + 5) won’t work. We can however,make it (12y - 5)(12y – 5), which will achieve our goalsperfectly.