Factor 8x^2-18xy+9y^2

$8 x^{2} - 18 x y + 9 y^{2}$

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 $a \cdot c = 8 \cdot 9 = 72$ and whose sum is $b = - 18$ .

Reorder terms.

$8 x^{2} + 9 y^{2} - 18 x y$

Reorder $9 y^{2}$ and $- 18 x y$ .

$8 x^{2} - 18 x y + 9 y^{2}$

Factor $- 18$ out of $- 18 x y$ .

$8 x^{2} - 18 (x y) + 9 y^{2}$

Rewrite $- 18$ as $- 6$ plus $- 12$

$8 x^{2} + (- 6 - 12) (x y) + 9 y^{2}$

Apply the distributive property.

$8 x^{2} - 6 (x y) - 12 (x y) + 9 y^{2}$

Remove unnecessary parentheses.

$8 x^{2} - 6 x y - 12 (x y) + 9 y^{2}$

Remove unnecessary parentheses.

$8 x^{2} - 6 x y - 12 x y + 9 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} - 6 x y) - 12 x y + 9 y^{2}$

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

$2 x (4 x - 3 y) - 3 y (4 x - 3 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 3 y$ .

$(4 x - 3 y) (2 x - 3 y)$

Factor 8x^2-18xy+9y^2

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