Factor x^2+11xy+18y^2

$x^{2} + 11 x y + 18 y^{2}$

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.

$x^{2} + 18 y^{2} + 11 x y$

Reorder $18 y^{2}$ and $11 x y$ .

$x^{2} + 11 x y + 18 y^{2}$

Factor $11$ out of $11 x y$ .

$x^{2} + 11 (x y) + 18 y^{2}$

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

$x^{2} + (2 + 9) (x y) + 18 y^{2}$

Apply the distributive property.

$x^{2} + 2 (x y) + 9 (x y) + 18 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 2 x y + 9 (x y) + 18 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 2 x y + 9 x y + 18 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} + 2 x y) + 9 x y + 18 y^{2}$

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

$x (x + 2 y) + 9 y (x + 2 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x + 2 y$ .

$(x + 2 y) (x + 9 y)$

Factor x^2+11xy+18y^2

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