Factor 125-27w^3 - MathMaster

$125 - 27 w^{3}$

Rewrite $125$ as $5^{3}$ .

$5^{3} - 27 w^{3}$

Rewrite $27 w^{3}$ as ${(3 w)}^{3}$ .

$5^{3} - {(3 w)}^{3}$

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 5$ and $b = 3 w$ .

$(5 - (3 w)) (5^{2} + 5 (3 w) + {(3 w)}^{2})$

Simplify.

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Multiply $3$ by $- 1$ .

$(5 - 3 w) (5^{2} + 5 (3 w) + {(3 w)}^{2})$

Raise $5$ to the power of $2$ .

$(5 - 3 w) (25 + 5 (3 w) + {(3 w)}^{2})$

Multiply $3$ by $5$ .

$(5 - 3 w) (25 + 15 w + {(3 w)}^{2})$

Apply the product rule to $3 w$ .

$(5 - 3 w) (25 + 15 w + 3^{2} w^{2})$

Raise $3$ to the power of $2$ .

$(5 - 3 w) (25 + 15 w + 9 w^{2})$

Factor 125-27w^3

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