Factor 2x^2-xy-28y^2

$2 x^{2} - x y - 28 y^{2}$

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 $a \cdot c = 2 \cdot - 28 = - 56$ and whose sum is $b = - 1$ .

Reorder terms.

$2 x^{2} - 28 y^{2} - x y$

Reorder $- 28 y^{2}$ and $- x y$ .

$2 x^{2} - x y - 28 y^{2}$

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

$2 x^{2} - (x y) - 28 y^{2}$

Rewrite $- 1$ as $7$ plus $- 8$

$2 x^{2} + (7 - 8) (x y) - 28 y^{2}$

Apply the distributive property.

$2 x^{2} + 7 (x y) - 8 (x y) - 28 y^{2}$

Remove unnecessary parentheses.

$2 x^{2} + 7 x y - 8 (x y) - 28 y^{2}$

Remove unnecessary parentheses.

$2 x^{2} + 7 x y - 8 x y - 28 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 7 x y) - 8 x y - 28 y^{2}$

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

$x (2 x + 7 y) - 4 y (2 x + 7 y)$

Step 3

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

$(2 x + 7 y) (x - 4 y)$

Factor 2x^2-xy-28y^2

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