Factor 125-27v^3

$125 - 27 v^{3}$

Step 1

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

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

Step 2

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

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

Step 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 $b = 3 v$ .

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

Step 4

Simplify.

Multiply $3$ by $- 1$ .

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

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

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

Multiply $3$ by $5$ .

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

Apply the product rule to $3 v$ .

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

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

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

Factor 125-27v^3

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