SOLUTION: Can you show me a step-by-step process on how to factor this? 25-(x+2)^2

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Question 928738: Can you show me a step-by-step process on how to factor this?
25-(x+2)^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
25-%28x%2B2%29%5E2+=+5%5E2-%28x%2B2%29%5E2

5%5E2-%28x%2B2%29%5E2 is in the form a%5E2+-+b%5E2 where a+=+5 and b+=+x%2B2

use the formula a%5E2+-+b%5E2+=+%28a-b%29%28a%2Bb%29 to get...


a%5E2+-+b%5E2+=+%28a-b%29%28a%2Bb%29

5%5E2-%28x%2B2%29%5E2+=+%285-%28x%2B2%29%29%285%2B%28x%2B2%29%29 Plug in a+=+5 and b+=+x%2B2

5%5E2-%28x%2B2%29%5E2+=+%285-x-2%29%285%2Bx%2B2%29

5%5E2-%28x%2B2%29%5E2+=+%283-x%29%287%2Bx%29

25-%28x%2B2%29%5E2+=+%283-x%29%287%2Bx%29


Therefore, 25-%28x%2B2%29%5E2 factors to %283-x%29%287%2Bx%29 which is equivalent to -%28x-3%29%287%2Bx%29 (I factored a negative out of 3-x to get -%28x-3%29)

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