Factor 64x^3-y^6 - Math solver

$64 x^{3} - y^{6}$

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

${(4 x)}^{3} - y^{6}$

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

${(4 x)}^{3} - {(y^{2})}^{3}$

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 $a = 4 x$ and $b = y^{2}$ .

$(4 x - y^{2}) ({(4 x)}^{2} + 4 x y^{2} + {(y^{2})}^{2})$

Simplify.

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Apply the product rule to $4 x$ .

$(4 x - y^{2}) (4^{2} x^{2} + 4 x y^{2} + {(y^{2})}^{2})$

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

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

Multiply the exponents in ${(y^{2})}^{2}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $2$ by $2$ .

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

Factor 64x^3-y^6

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