Factor 9x^2-27xy-36y^2

$9 x^{2} - 27 x y - 36 y^{2}$

Step 1

Factor $9$ out of $9 x^{2} - 27 x y - 36 y^{2}$ .

Factor $9$ out of $9 x^{2}$ .

$9 (x^{2}) - 27 x y - 36 y^{2}$

Factor $9$ out of $- 27 x y$ .

$9 (x^{2}) + 9 (- 3 x y) - 36 y^{2}$

Factor $9$ out of $- 36 y^{2}$ .

$9 (x^{2}) + 9 (- 3 x y) + 9 (- 4 y^{2})$

Factor $9$ out of $9 (x^{2}) + 9 (- 3 x y)$ .

$9 (x^{2} - 3 x y) + 9 (- 4 y^{2})$

Factor $9$ out of $9 (x^{2} - 3 x y) + 9 (- 4 y^{2})$ .

$9 (x^{2} - 3 x y - 4 y^{2})$

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 1 \cdot - 4 = - 4$ and whose sum is $b = - 3$ .

Reorder terms.

$9 (x^{2} - 4 y^{2} - 3 x y)$

Reorder $- 4 y^{2}$ and $- 3 x y$ .

$9 (x^{2} - 3 x y - 4 y^{2})$

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

$9 (x^{2} - 3 (x y) - 4 y^{2})$

Rewrite $- 3$ as $1$ plus $- 4$

$9 (x^{2} + (1 - 4) (x y) - 4 y^{2})$

Apply the distributive property.

$9 (x^{2} + 1 (x y) - 4 (x y) - 4 y^{2})$

Multiply $x y$ by $1$ .

$9 (x^{2} + x y - 4 (x y) - 4 y^{2})$

Remove unnecessary parentheses.

$9 (x^{2} + x y - 4 x y - 4 y^{2})$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$9 ((x^{2} + x y) - 4 x y - 4 y^{2})$

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

$9 (x (x + y) - 4 y (x + y))$

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

$9 ((x + y) (x - 4 y))$

Remove unnecessary parentheses.

$9 (x + y) (x - 4 y)$

Factor 9x^2-27xy-36y^2

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