Factor 16x^3-2y^3

$16 x^{3} - 2 y^{3}$

Step 1

Factor $2$ out of $16 x^{3} - 2 y^{3}$ .

Factor $2$ out of $16 x^{3}$ .

$2 (8 x^{3}) - 2 y^{3}$

Factor $2$ out of $- 2 y^{3}$ .

$2 (8 x^{3}) + 2 (- y^{3})$

Factor $2$ out of $2 (8 x^{3}) + 2 (- y^{3})$ .

$2 (8 x^{3} - y^{3})$

Step 2

Rewrite $8 x^{3}$ as ${(2 x)}^{3}$ .

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

Step 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 $a = 2 x$ and $b = y$ .

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

Step 4

Factor.

Simplify.

Apply the product rule to $2 x$ .

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

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

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

Remove unnecessary parentheses.

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

Factor 16x^3-2y^3

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