Factor a^2-13ab+42b^2

$a^{2} - 13 a b + 42 b^{2}$

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 $b = - 13$ .

Reorder terms.

$a^{2} + 42 b^{2} - 13 a b$

Reorder $42 b^{2}$ and $- 13 a b$ .

$a^{2} - 13 a b + 42 b^{2}$

Factor $- 13$ out of $- 13 a b$ .

$a^{2} - 13 (a b) + 42 b^{2}$

Rewrite $- 13$ 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^2-13ab+42b^2

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