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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