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

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Answer 1 · 2015-12-14T22:21:19

Use the sum of cubes identity to find:

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

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

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

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

$125x^3+64$

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

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

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

How do you factor 125x^3+64 125x^3+64?