Factor 2x^2+3xy-2y^2

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

Step 1

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 $a \cdot c = 2 \cdot - 2 = - 4$ and whose sum is $b = 3$ .

Reorder terms.

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

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

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

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

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

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

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

Apply the distributive property.

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Step 2

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

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

Factor 2x^2+3xy-2y^2

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