Factor 2x^3y-4x^2y^2+8xy-16y^2

$2 x^{3} y - 4 x^{2} y^{2} + 8 x y - 16 y^{2}$

Step 1

Factor $2 y$ out of $2 x^{3} y - 4 x^{2} y^{2} + 8 x y - 16 y^{2}$ .

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

$2 y (x^{3}) - 4 x^{2} y^{2} + 8 x y - 16 y^{2}$

Factor $2 y$ out of $- 4 x^{2} y^{2}$ .

$2 y (x^{3}) + 2 y (- 2 x^{2} y) + 8 x y - 16 y^{2}$

Factor $2 y$ out of $8 x y$ .

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

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

$2 y (x^{3}) + 2 y (- 2 x^{2} y) + 2 y (4 x) + 2 y (- 8 y)$

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

$2 y (x^{3} - 2 x^{2} y) + 2 y (4 x) + 2 y (- 8 y)$

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

$2 y (x^{3} - 2 x^{2} y + 4 x) + 2 y (- 8 y)$

Factor $2 y$ out of $2 y (x^{3} - 2 x^{2} y + 4 x) + 2 y (- 8 y)$ .

$2 y (x^{3} - 2 x^{2} y + 4 x - 8 y)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 y ((x^{3} - 2 x^{2} y) + 4 x - 8 y)$

Factor out the greatest common factor (GCF) from each group.

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

Step 3

Factor.

Factor the polynomial by factoring out the greatest common factor, $x - 2 y$ .

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

Remove unnecessary parentheses.

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