SOLUTION: Factor -c^3-125

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Question 371134: Factor -c^3-125
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
We can factor this two ways.
1. Factor out a -1:
%28-1%29%28c%5E3%2B125%29
then factor as a sum of cubes (since 125+=+5%5E3). The pattern for sum of cubes is: a%5E3%2Bb%5E3+=+%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29. Using this on c%5E3%2B125 we get:
%28-1%29%28%28c%29%2B%285%29%29%28%28c%29%5E2+-+%28c%29%285%29+%2B+%285%29%5E2%29
which simplifies to:
%28-1%29%28c%2B5%29%28c%5E2+-+5c+%2B+25%29

2. Factor as a difference of cubes (since -c%5E3+=+%28-c%29%5E3 and 125 is still a perfect cube. The pattern for difference of cubes is: a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29. Using this on -c%5E3-125 we get:
%28%28-c%29-%285%29%29%28%28-c%29%5E2%2B%28-c%29%285%29%2B%285%29%5E2%29
which simplifies to:
%28-c-5%29%28c%5E2-5c%2B25%29

Either answer is correct. They are equivalent.