How do you factor $u^{3} - 125 v^{3}$ $u^3 - 125v^3$ ?

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How do you factor $u^{3} - 125 v^{3}$ $u^3 - 125v^3$ ?

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Answer 1 · 2016-03-05T20:24:05

$u^{3} - {(5 v)}^{3} = (u - 5 v) (u^{2} + 5 u v + 25 v^{2})$ $u^3-(5v)^3=(u-5v)(u^2+5uv+25v^2)$

Explanation:

Use the difference of two cubes formula. That is, $(x^{3} - y^{3}) = (x - y) (x^{2} + x y + y^{2})$ $(x^3-y^3)=(x-y)(x^2+xy+y^2)$ . So first write out the problem as a difference of two cubes then apply the formula.

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How do you factor $u^{3} - 125 v^{3}$ $u^3 - 125v^3$ ?

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