Factor 125-27x^3

$125 - 27 x^{3}$

Step 1

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

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

Step 2

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

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

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 $b = 3 x$ .

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

Step 4

Simplify.

Multiply $3$ by $- 1$ .

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

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

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

Multiply $3$ by $5$ .

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

Apply the product rule to $3 x$ .

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

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

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

Factor 125-27x^3

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