Factor a^2-9ab+18b^2

$a^{2} - 9 a b + 18 b^{2}$

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 $a \cdot c = 1 \cdot 18 = 18$ and whose sum is $b = - 9$ .

Reorder terms.

$a^{2} + 18 b^{2} - 9 a b$

Reorder $18 b^{2}$ and $- 9 a b$ .

$a^{2} - 9 a b + 18 b^{2}$

Factor $- 9$ out of $- 9 a b$ .

$a^{2} - 9 (a b) + 18 b^{2}$

Rewrite $- 9$ as $- 3$ plus $- 6$

$a^{2} + (- 3 - 6) (a b) + 18 b^{2}$

Apply the distributive property.

$a^{2} - 3 (a b) - 6 (a b) + 18 b^{2}$

Remove unnecessary parentheses.

$a^{2} - 3 a b - 6 (a b) + 18 b^{2}$

Remove unnecessary parentheses.

$a^{2} - 3 a b - 6 a b + 18 b^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(a^{2} - 3 a b) - 6 a b + 18 b^{2}$

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

$a (a - 3 b) - 6 b (a - 3 b)$

Step 3

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

$(a - 3 b) (a - 6 b)$

Factor a^2-9ab+18b^2

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