Factor -12x^4y-9x^3y^2+3x^2y^3

$- 12 x^{4} y - 9 x^{3} y^{2} + 3 x^{2} y^{3}$

Step 1

Factor $- 3 x^{2} y$ out of $- 12 x^{4} y - 9 x^{3} y^{2} + 3 x^{2} y^{3}$ .

Reorder the expression.

Move $- 12 x^{4} y$ .

$- 9 x^{3} y^{2} + 3 x^{2} y^{3} - 12 x^{4} y$

Reorder $- 9 x^{3} y^{2}$ and $3 x^{2} y^{3}$ .

$3 x^{2} y^{3} - 9 x^{3} y^{2} - 12 x^{4} y$

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

$- 3 x^{2} y (- 1 y^{2}) - 9 x^{3} y^{2} - 12 x^{4} y$

Factor $- 3 x^{2} y$ out of $- 9 x^{3} y^{2}$ .

$- 3 x^{2} y (- 1 y^{2}) - 3 x^{2} y (3 x y) - 12 x^{4} y$

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

$- 3 x^{2} y (- 1 y^{2}) - 3 x^{2} y (3 x y) - 3 x^{2} y (4 x^{2})$

Factor $- 3 x^{2} y$ out of $- 3 x^{2} y (- 1 y^{2}) - 3 x^{2} y (3 x y)$ .

$- 3 x^{2} y (- 1 y^{2} + 3 x y) - 3 x^{2} y (4 x^{2})$

Factor $- 3 x^{2} y$ out of $- 3 x^{2} y (- 1 y^{2} + 3 x y) - 3 x^{2} y (4 x^{2})$ .

$- 3 x^{2} y (- 1 y^{2} + 3 x y + 4 x^{2})$

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 $a \cdot c = 4 \cdot - 1 = - 4$ and whose sum is $b = 3$ .

Reorder terms.

$- 3 x^{2} y (4 x^{2} - 1 y^{2} + 3 x y)$

Reorder $- 1 y^{2}$ and $3 x y$ .

$- 3 x^{2} y (4 x^{2} + 3 x y - 1 y^{2})$

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

$- 3 x^{2} y (4 x^{2} + 3 (x y) - 1 y^{2})$

Rewrite $3$ as $- 1$ plus $4$

$- 3 x^{2} y (4 x^{2} + (- 1 + 4) (x y) - 1 y^{2})$

Apply the distributive property.

$- 3 x^{2} y (4 x^{2} - 1 (x y) + 4 (x y) - 1 y^{2})$

Remove unnecessary parentheses.

$- 3 x^{2} y (4 x^{2} - 1 x y + 4 (x y) - 1 y^{2})$

Remove unnecessary parentheses.

$- 3 x^{2} y (4 x^{2} - 1 x y + 4 x y - 1 y^{2})$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- 3 x^{2} y ((4 x^{2} - 1 x y) + 4 x y - 1 y^{2})$

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

$- 3 x^{2} y (x (4 x - 1 y) + y (4 x - 1 y))$

Factor the polynomial by factoring out the greatest common factor, $4 x - 1 y$ .

$- 3 x^{2} y ((4 x - 1 y) (x + y))$

Step 3

Factor.

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

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

Remove unnecessary parentheses.

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

Factor -12x^4y-9x^3y^2+3x^2y^3

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