Factor 64x^3+125 - MathMaster

$64 x^{3} + 125$

Rewrite $64 x^{3}$ as ${(4 x)}^{3}$ .

${(4 x)}^{3} + 125$

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

${(4 x)}^{3} + 5^{3}$

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 $a = 4 x$ and $b = 5$ .

$(4 x + 5) ({(4 x)}^{2} - (4 x) \cdot 5 + 5^{2})$

Simplify.

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Apply the product rule to $4 x$ .

$(4 x + 5) (4^{2} x^{2} - (4 x) \cdot 5 + 5^{2})$

Raise $4$ to the power of $2$ .

$(4 x + 5) (16 x^{2} - (4 x) \cdot 5 + 5^{2})$

Multiply $4$ by $- 1$ .

$(4 x + 5) (16 x^{2} - 4 x \cdot 5 + 5^{2})$

Multiply $5$ by $- 4$ .

$(4 x + 5) (16 x^{2} - 20 x + 5^{2})$

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

$(4 x + 5) (16 x^{2} - 20 x + 25)$

Factor 64x^3+125

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