Factor 7(x+y)^2+13y(x+y)-2y^2

$7 {(x + y)}^{2} + 13 y (x + y) - 2 y^{2}$

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 $a \cdot c = - 2 \cdot 7 = - 14$ and whose sum is $b = 13$ .

Reorder terms.

$- 2 y^{2} + 7 {(x + y)}^{2} + 13 y (x + y)$

Reorder $7 {(x + y)}^{2}$ and $13 y (x + y)$ .

$- 2 y^{2} + 13 y (x + y) + 7 {(x + y)}^{2}$

Factor $13$ out of $13 y (x + y)$ .

$- 2 y^{2} + 13 (y (x + y)) + 7 {(x + y)}^{2}$

Rewrite $13$ as $- 1$ plus $14$

$- 2 y^{2} + (- 1 + 14) (y (x + y)) + 7 {(x + y)}^{2}$

Apply the distributive property.

$- 2 y^{2} - 1 (y (x + y)) + 14 (y (x + y)) + 7 {(x + y)}^{2}$

Remove unnecessary parentheses.

$- 2 y^{2} - 1 y (x + y) + 14 (y (x + y)) + 7 {(x + y)}^{2}$

Remove unnecessary parentheses.

$- 2 y^{2} - 1 y (x + y) + 14 y (x + y) + 7 {(x + y)}^{2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- 2 y^{2} - 1 y (x + y)) + 14 y (x + y) + 7 {(x + y)}^{2}$

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

$y (- 2 y - 1 (x + y)) - 7 (x + y) (- 2 y - (x + y))$

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

$(- 2 y - 1 (x + y)) (y - 7 (x + y))$

Apply the distributive property.

$(- 2 y - 1 x - 1 y) (y - 7 (x + y))$

Rewrite $- 1 x$ as $- x$ .

$(- 2 y - x - 1 y) (y - 7 (x + y))$

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

$(- 2 y - x - y) (y - 7 (x + y))$

Subtract $y$ from $- 2 y$ .

$(- x - 3 y) (y - 7 (x + y))$

Apply the distributive property.

$(- x - 3 y) (y - 7 x - 7 y)$

Subtract $7 y$ from $y$ .

$(- x - 3 y) (- 7 x - 6 y)$

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

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

$(- (x) - 3 y) (- 7 x - 6 y)$

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

$(- (x) - (3 y)) (- 7 x - 6 y)$

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

$- (x + 3 y) (- 7 x - 6 y)$

Factor.

Factor $- 1$ out of $- 7 x - 6 y$ .

Factor $- 1$ out of $- 7 x$ .

$- (x + 3 y) (- (7 x) - 6 y)$

Factor $- 1$ out of $- 6 y$ .

$- (x + 3 y) (- (7 x) - (6 y))$

Factor $- 1$ out of $- (7 x) - (6 y)$ .

$- (x + 3 y) (- (7 x + 6 y))$

Remove unnecessary parentheses.

$- (x + 3 y) \cdot - 1 (7 x + 6 y)$

Combine exponents.

Factor out negative.

$- ((x + 3 y) \cdot - 1 (7 x + 6 y))$

Multiply $- 1$ by $- 1$ .

$1 ((x + 3 y) (7 x + 6 y))$

Multiply $x + 3 y$ by $1$ .

$(x + 3 y) (7 x + 6 y)$

Factor 7(x+y)^2+13y(x+y)-2y^2

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