Factor x^2+9xy-36y^2

$x^{2} + 9 x y - 36 y^{2}$

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 $a \cdot c = 1 \cdot - 36 = - 36$ and whose sum is $b = 9$ .

Reorder terms.

$x^{2} - 36 y^{2} + 9 x y$

Reorder $- 36 y^{2}$ and $9 x y$ .

$x^{2} + 9 x y - 36 y^{2}$

Factor $9$ out of $9 x y$ .

$x^{2} + 9 (x y) - 36 y^{2}$

Rewrite $9$ as $- 3$ plus $12$

$x^{2} + (- 3 + 12) (x y) - 36 y^{2}$

Apply the distributive property.

$x^{2} - 3 (x y) + 12 (x y) - 36 y^{2}$

Remove unnecessary parentheses.

$x^{2} - 3 x y + 12 (x y) - 36 y^{2}$

Remove unnecessary parentheses.

$x^{2} - 3 x y + 12 x y - 36 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} - 3 x y) + 12 x y - 36 y^{2}$

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

$x (x - 3 y) + 12 y (x - 3 y)$

Step 3

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

$(x - 3 y) (x + 12 y)$

Factor x^2+9xy-36y^2

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