How do you factor $125 x^{3} + 64$ $125x^3+64$ ?

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How do you factor $125 x^{3} + 64$ $125x^3+64$ ?

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Answer 1 · 2015-12-14T22:21:19

Use the sum of cubes identity to find:

$125 x^{3} + 64 = (5 x + 4) (25 x^{2} - 20 x + 16)$ $125x^3+64=(5x+4)(25x^2-20x+16)$

Explanation:

Both $125 x^{3} = {(5 x)}^{3}$ $125x^3 = (5x)^3$ and $64 = 4^{3}$ $64 = 4^3$ are perfect cubes, so this is a natural case for the sum of cubes identity:

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ $a^3+b^3=(a+b)(a^2-ab+b^2)$

With $a = 5 x$ $a=5x$ and $b = 4$ $b=4$ we find:

$125 x^{3} + 64$ $125x^3+64$

$= {(5 x)}^{3} + 4^{3}$ $=(5x)^3+4^3$

$= (5 x + 4) ({(5 x)}^{2} - (5 x) (4) + 4^{2})$ $= (5x+4)((5x)^2-(5x)(4)+4^2)$

$= (5 x + 4) (25 x^{2} - 20 x + 16)$ $=(5x+4)(25x^2-20x+16)$

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How do you factor $125 x^{3} + 64$ $125x^3+64$ ?

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