Factor 9x^2-6xy-8y^2

$9 x^{2} - 6 x y - 8 y^{2}$

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 $a \cdot c = 9 \cdot - 8 = - 72$ and whose sum is $b = - 6$ .

Reorder terms.

$9 x^{2} - 8 y^{2} - 6 x y$

Reorder $- 8 y^{2}$ and $- 6 x y$ .

$9 x^{2} - 6 x y - 8 y^{2}$

Factor $- 6$ out of $- 6 x y$ .

$9 x^{2} - 6 (x y) - 8 y^{2}$

Rewrite $- 6$ as $6$ plus $- 12$

$9 x^{2} + (6 - 12) (x y) - 8 y^{2}$

Apply the distributive property.

$9 x^{2} + 6 (x y) - 12 (x y) - 8 y^{2}$

Remove unnecessary parentheses.

$9 x^{2} + 6 x y - 12 (x y) - 8 y^{2}$

Remove unnecessary parentheses.

$9 x^{2} + 6 x y - 12 x y - 8 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 x^{2} + 6 x y) - 12 x y - 8 y^{2}$

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

$3 x (3 x + 2 y) - 4 y (3 x + 2 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + 2 y$ .

$(3 x + 2 y) (3 x - 4 y)$

Factor 9x^2-6xy-8y^2

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