SOLUTION: Factor completely: 64x^3+343 factors of 64=1,2,4,8,16,32,64 ". ". 343=1,7,49 (8x^2+7)(8x+49) can't foil & I am stuck!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor completely: 64x^3+343 factors of 64=1,2,4,8,16,32,64 ". ". 343=1,7,49 (8x^2+7)(8x+49) can't foil & I am stuck!      Log On


   

Question 258302: Factor completely: 64x^3+343
factors of 64=1,2,4,8,16,32,64
". ". 343=1,7,49
(8x^2+7)(8x+49) can't foil & I am stuck!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factor completely: 64x^3+343
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It's the sum of 2 cubes.
a%5E3+%2B+b%5E3+=+%28a%2Bb%29%2A%28a%5E2+-+ab+%2B+b%5E2%29
Sub 4x for a, and 7 for b
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64x%5E3+%2B+343+=+%284x%2B7%29%2A%2816x%5E2+-+28x+%2B+49%29
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The difference of 2 cubes is similar:
a%5E3-b%5E3+=+%28a-b%29%2A%28a%5E2+%2B+ab+%2B+b%5E2%29
The difference of any 2 odd powers is also similar.