How do you factor $5 w^{3} - 1080$ $5w^3-1080$ ?

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How do you factor $5 w^{3} - 1080$ $5w^3-1080$ ?

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Answer 1 · 2017-02-16T01:31:47

$5 w^{3} - 1080 = 5 (w - 6) (w^{2} + 6 w + 36)$ $5w^3-1080 = 5(w-6)(w^2+6w+36)$

Explanation:

The difference of cubes identity can be written:

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

We can use this with $a = w$ $a=w$ and $b = 6$ $b=6$ as follows:

$5 w^{3} - 1080 = 5 (w^{3} - 216)$ $5w^3-1080 = 5(w^3-216)$

$5 w^{3} - 1080 = 5 (w^{3} - 6^{3})$ $color(white)(5w^3-1080) = 5(w^3-6^3)$

$5 w^{3} - 1080 = 5 (w - 6) (w^{2} + 6 w + 6^{2})$ $color(white)(5w^3-1080) = 5(w-6)(w^2+6w+6^2)$

$5 w^{3} - 1080 = 5 (w - 6) (w^{2} + 6 w + 36)$ $color(white)(5w^3-1080) = 5(w-6)(w^2+6w+36)$

The remaining quadratic factor has no linear factors with Real coefficients.

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How do you factor $5 w^{3} - 1080$ $5w^3-1080$ ?

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