Factor 2x^2+7xy-15y^2

$2 x^{2} + 7 x y - 15 y^{2}$

Step 1

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 $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = 7$ .

Reorder terms.

$2 x^{2} - 15 y^{2} + 7 x y$

Reorder $- 15 y^{2}$ and $7 x y$ .

$2 x^{2} + 7 x y - 15 y^{2}$

Factor $7$ out of $7 x y$ .

$2 x^{2} + 7 (x y) - 15 y^{2}$

Rewrite $7$ as $- 3$ plus $10$

$2 x^{2} + (- 3 + 10) (x y) - 15 y^{2}$

Apply the distributive property.

$2 x^{2} - 3 (x y) + 10 (x y) - 15 y^{2}$

Remove unnecessary parentheses.

$2 x^{2} - 3 x y + 10 (x y) - 15 y^{2}$

Remove unnecessary parentheses.

$2 x^{2} - 3 x y + 10 x y - 15 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 3 x y) + 10 x y - 15 y^{2}$

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

$x (2 x - 3 y) + 5 y (2 x - 3 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x - 3 y$ .

$(2 x - 3 y) (x + 5 y)$

Factor 2x^2+7xy-15y^2

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