Factor 2x^2-3xy-35y^2

$2 x^{2} - 3 x y - 35 y^{2}$

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 $a \cdot c = 2 \cdot - 35 = - 70$ and whose sum is $b = - 3$ .

Reorder terms.

$2 x^{2} - 35 y^{2} - 3 x y$

Reorder $- 35 y^{2}$ and $- 3 x y$ .

$2 x^{2} - 3 x y - 35 y^{2}$

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

$2 x^{2} - 3 (x y) - 35 y^{2}$

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

$2 x^{2} + (7 - 10) (x y) - 35 y^{2}$

Apply the distributive property.

$2 x^{2} + 7 (x y) - 10 (x y) - 35 y^{2}$

Remove unnecessary parentheses.

$2 x^{2} + 7 x y - 10 (x y) - 35 y^{2}$

Remove unnecessary parentheses.

$2 x^{2} + 7 x y - 10 x y - 35 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 7 x y) - 10 x y - 35 y^{2}$

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

$x (2 x + 7 y) - 5 y (2 x + 7 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x + 7 y$ .

$(2 x + 7 y) (x - 5 y)$

Factor 2x^2-3xy-35y^2

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