Factor x^2+xy-2y^2

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

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 $a \cdot c = 1 \cdot - 2 = - 2$ and whose sum is $b = 1$ .

Reorder terms.

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

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

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

Factor $1$ out of $x y$ .

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

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

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

Apply the distributive property.

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Step 2

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

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

Factor x^2+xy-2y^2

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