Factor 16x^2-16xy^3+4y^6

$16 x^{2} - 16 x y^{3} + 4 y^{6}$

Factor $4$ out of $16 x^{2} - 16 x y^{3} + 4 y^{6}$ .

Factor $4$ out of $16 x^{2}$ .

$4 (4 x^{2}) - 16 x y^{3} + 4 y^{6}$

Factor $4$ out of $- 16 x y^{3}$ .

$4 (4 x^{2}) + 4 (- 4 x y^{3}) + 4 y^{6}$

Factor $4$ out of $4 y^{6}$ .

$4 (4 x^{2}) + 4 (- 4 x y^{3}) + 4 (y^{6})$

Factor $4$ out of $4 (4 x^{2}) + 4 (- 4 x y^{3})$ .

$4 (4 x^{2} - 4 x y^{3}) + 4 (y^{6})$

Factor $4$ out of $4 (4 x^{2} - 4 x y^{3}) + 4 (y^{6})$ .

$4 (4 x^{2} - 4 x y^{3} + y^{6})$

Factor using the perfect square rule.

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$4 ({(2 x)}^{2} - 4 x y^{3} + y^{6})$

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

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

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x y^{3} = 2 \cdot (2 x) \cdot y^{3}$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 x$ and $b = y^{3}$ .

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