Factoring Special Products in Difference of Squares
Problem 1 9x2-4
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.
Example Problems a2 – 81 36m2 – 25 4x2 – y2 a2 + 64 Remember that both must be PERFECT squares.
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.
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.
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.
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).
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.
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.