Factor a^2+11ab+18b^2

$a^{2} + 11 a b + 18 b^{2}$

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 $b = 11$ .

Reorder terms.

$a^{2} + 18 b^{2} + 11 a b$

Reorder $18 b^{2}$ and $11 a b$ .

$a^{2} + 11 a b + 18 b^{2}$

Factor $11$ out of $11 a b$ .

$a^{2} + 11 (a b) + 18 b^{2}$

Rewrite $11$ as $2$ plus $9$

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

Apply the distributive property.

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$a (a + 2 b) + 9 b (a + 2 b)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $a + 2 b$ .

$(a + 2 b) (a + 9 b)$

Factor a^2+11ab+18b^2

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