Factor -4xy^3+12x^2y^2-8x^3y

$- 4 x y^{3} + 12 x^{2} y^{2} - 8 x^{3} y$

Step 1

Factor $- 4 x y$ out of $- 4 x y^{3} + 12 x^{2} y^{2} - 8 x^{3} y$ .

Reorder the expression.

Move $- 4 x y^{3}$ .

$12 x^{2} y^{2} - 8 x^{3} y - 4 x y^{3}$

Reorder $12 x^{2} y^{2}$ and $- 8 x^{3} y$ .

$- 8 x^{3} y + 12 x^{2} y^{2} - 4 x y^{3}$

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

$- 4 x y (2 x^{2}) + 12 x^{2} y^{2} - 4 x y^{3}$

Factor $- 4 x y$ out of $12 x^{2} y^{2}$ .

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

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

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

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

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

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

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

Step 2

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 1 = 2$ and whose sum is $b = - 3$ .

Reorder terms.

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

Reorder $y^{2}$ and $- 3 x y$ .

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

Factor $- 3$ out of $- 3 x y$ .

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

Rewrite $- 3$ as $- 1$ plus $- 2$

$- 4 x y (2 x^{2} + (- 1 - 2) (x y) + y^{2})$

Apply the distributive property.

$- 4 x y (2 x^{2} - 1 (x y) - 2 (x y) + y^{2})$

Remove unnecessary parentheses.

$- 4 x y (2 x^{2} - 1 x y - 2 (x y) + y^{2})$

Remove unnecessary parentheses.

$- 4 x y (2 x^{2} - 1 x y - 2 x y + y^{2})$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- 4 x y ((2 x^{2} - 1 x y) - 2 x y + y^{2})$

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

$- 4 x y (x (2 x - 1 y) - y (2 x - y))$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1 y$ .

$- 4 x y ((2 x - 1 y) (x - y))$

Step 3

Factor.

Rewrite $- 1 y$ as $- y$ .

$- 4 x y ((2 x - y) (x - y))$

Remove unnecessary parentheses.

$- 4 x y (2 x - y) (x - y)$

Factor -4xy^3+12x^2y^2-8x^3y

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