Factor a^2-ab-42b^2

$a^{2} - a b - 42 b^{2}$

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 $a \cdot c = 1 \cdot - 42 = - 42$ and whose sum is $b = - 1$ .

Reorder terms.

$a^{2} - 42 b^{2} - a b$

Reorder $- 42 b^{2}$ and $- a b$ .

$a^{2} - a b - 42 b^{2}$

Factor $- 1$ out of $- a b$ .

$a^{2} - (a b) - 42 b^{2}$

Rewrite $- 1$ as $6$ plus $- 7$

$a^{2} + (6 - 7) (a b) - 42 b^{2}$

Apply the distributive property.

$a^{2} + 6 (a b) - 7 (a b) - 42 b^{2}$

Remove unnecessary parentheses.

$a^{2} + 6 a b - 7 (a b) - 42 b^{2}$

Remove unnecessary parentheses.

$a^{2} + 6 a b - 7 a b - 42 b^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(a^{2} + 6 a b) - 7 a b - 42 b^{2}$

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

$a (a + 6 b) - 7 b (a + 6 b)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $a + 6 b$ .

$(a + 6 b) (a - 7 b)$

Factor a^2-ab-42b^2

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