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 sum 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.

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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