Factor 64-125r^3 - Math solver

$64 - 125 r^{3}$

Rewrite $64$ as $4^{3}$ .

$4^{3} - 125 r^{3}$

Rewrite $125 r^{3}$ as ${(5 r)}^{3}$ .

$4^{3} - {(5 r)}^{3}$

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

$(4 - (5 r)) (4^{2} + 4 (5 r) + {(5 r)}^{2})$

Simplify.

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Multiply $5$ by $- 1$ .

$(4 - 5 r) (4^{2} + 4 (5 r) + {(5 r)}^{2})$

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

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

Multiply $5$ by $4$ .

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

Apply the product rule to $5 r$ .

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

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

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

Factor 64-125r^3

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