Factor x^2-xy-6y^2

$x^{2} - x y - 6 y^{2}$

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 $a \cdot c = 1 \cdot - 6 = - 6$ and whose sum is $b = - 1$ .

Reorder terms.

$x^{2} - 6 y^{2} - x y$

Reorder $- 6 y^{2}$ and $- x y$ .

$x^{2} - x y - 6 y^{2}$

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

$x^{2} - (x y) - 6 y^{2}$

Rewrite $- 1$ as $2$ plus $- 3$

$x^{2} + (2 - 3) (x y) - 6 y^{2}$

Apply the distributive property.

$x^{2} + 2 (x y) - 3 (x y) - 6 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 2 x y - 3 (x y) - 6 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 2 x y - 3 x y - 6 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} + 2 x y) - 3 x y - 6 y^{2}$

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

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

Step 3

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

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

Factor x^2-xy-6y^2

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