Factor x^2+7xy-18y^2

$x^{2} + 7 x y - 18 y^{2}$

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 $a \cdot c = 1 \cdot - 18 = - 18$ and whose sum is $b = 7$ .

Reorder terms.

$x^{2} - 18 y^{2} + 7 x y$

Reorder $- 18 y^{2}$ and $7 x y$ .

$x^{2} + 7 x y - 18 y^{2}$

Factor $7$ out of $7 x y$ .

$x^{2} + 7 (x y) - 18 y^{2}$

Rewrite $7$ as $- 2$ plus $9$

$x^{2} + (- 2 + 9) (x y) - 18 y^{2}$

Apply the distributive property.

$x^{2} - 2 (x y) + 9 (x y) - 18 y^{2}$

Remove unnecessary parentheses.

$x^{2} - 2 x y + 9 (x y) - 18 y^{2}$

Remove unnecessary parentheses.

$x^{2} - 2 x y + 9 x y - 18 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} - 2 x y) + 9 x y - 18 y^{2}$

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

$x (x - 2 y) + 9 y (x - 2 y)$

Step 3

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

$(x - 2 y) (x + 9 y)$

Factor x^2+7xy-18y^2

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