Factor 5a^2-7ab-6b^2

$5 a^{2} - 7 a b - 6 b^{2}$

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 $a \cdot c = 5 \cdot - 6 = - 30$ and whose sum is $b = - 7$ .

Reorder terms.

$5 a^{2} - 6 b^{2} - 7 a b$

Reorder $- 6 b^{2}$ and $- 7 a b$ .

$5 a^{2} - 7 a b - 6 b^{2}$

Factor $- 7$ out of $- 7 a b$ .

$5 a^{2} - 7 (a b) - 6 b^{2}$

Rewrite $- 7$ as $3$ plus $- 10$

$5 a^{2} + (3 - 10) (a b) - 6 b^{2}$

Apply the distributive property.

$5 a^{2} + 3 (a b) - 10 (a b) - 6 b^{2}$

Remove unnecessary parentheses.

$5 a^{2} + 3 a b - 10 (a b) - 6 b^{2}$

Remove unnecessary parentheses.

$5 a^{2} + 3 a b - 10 a b - 6 b^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 a^{2} + 3 a b) - 10 a b - 6 b^{2}$

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

$a (5 a + 3 b) - 2 b (5 a + 3 b)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 a + 3 b$ .

$(5 a + 3 b) (a - 2 b)$

Factor 5a^2-7ab-6b^2

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