SOLUTION: Factor the following y^3+8 10x^3+80 25x^2+60x+36 81x^2_1

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Question 691006: Factor the following
y^3+8
10x^3+80
25x^2+60x+36
81x^2_1
Found 2 solutions by jim_thompson5910, fcabanski:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y^3+8

y^3+2^3

(y+2)(y^2+2y+2^2)

(y+2)(y^2+2y+4)

Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3+%2B+y%5E3+=+%28x%2By%29%28x%5E2+-xy+%2B+y%5E2%29 and x%5E3+-+y%5E3+=+%28x-y%29%28x%5E2+%2B+xy+%2B+y%5E2%29. These are the formulas for sum of cubes and difference of cubes. Jim Thompson's solution has a mistake.
y%5E3+%2B+8+=+y%5E3+%2B+2%5E3+=+%28y%2B2%29%28y%5E2+-2y+%2B4%29


10x%5E3%2B80+=+10%28x%5E3+%2B2%5E3%29+=+10%28x%2B2%29%28x%5E2+-+2x+%2B4%29


%28a%2Bb%29%5E2+=+a%5E2+%2B2ab+%2B+b%5E2 and %28a-b%29%5E2+=+a%5E2+-+2ab+%2Bb%5E2 and a%5E2+-+b%5E2+=%28a%2Bb%29%28a-b%29


25x%5E2%2B60x%2B36 if a=5x and b=6 this is %285x%29%5E2+%2B2%285x%29%286%29+%2B+6%5E2=%285x%2B6%29%5E2+=+%285x%2B6%29%285x%2B6%29


81x%5E2+-+1 if a=9x and b =1 this is %289x%29%5E2+-%281%29%5E2+=+%289x%2B1%29%289x-1%29

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