Factor 125+27u^3

$125 + 27 u^{3}$

Step 1

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

$5^{3} + 27 u^{3}$

Step 2

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

$5^{3} + {(3 u)}^{3}$

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 $b = 3 u$ .

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

Step 4

Simplify.

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

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

Multiply $3$ by $- 5$ .

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

Apply the product rule to $3 u$ .

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

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

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

Factor 125+27u^3

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