Factor y^2+xy-6x^2

$y^{2} + x y - 6 x^{2}$

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 $a \cdot c = - 6 \cdot 1 = - 6$ and whose sum is $b = 1$ .

Reorder terms.

$- 6 x^{2} + y^{2} + x y$

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

$- 6 x^{2} + x y + y^{2}$

Factor $1$ out of $x y$ .

$- 6 x^{2} + 1 (x y) + y^{2}$

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

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

Apply the distributive property.

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 x (- 3 x - 1 y) - y (- 3 x - y)$

Factor the polynomial by factoring out the greatest common factor, $- 3 x - 1 y$ .

$(- 3 x - 1 y) (2 x - y)$

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

$(- 3 x - y) (2 x - y)$

Factor $- 1$ out of $- 3 x - y$ .

Factor $- 1$ out of $- 3 x$ .

$(- (3 x) - y) (2 x - y)$

Factor $- 1$ out of $- y$ .

$(- (3 x) - (y)) (2 x - y)$

Factor $- 1$ out of $- (3 x) - (y)$ .

$- (3 x + y) (2 x - y)$

Factor y^2+xy-6x^2

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