Factor 2x^2-3xy+y^2

$2 x^{2} - 3 x y + y^{2}$

Step 1

Factor by grouping.

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 $a \cdot c = 2 \cdot 1 = 2$ and whose sum is $b = - 3$ .

Reorder terms.

$2 x^{2} + y^{2} - 3 x y$

Reorder $y^{2}$ and $- 3 x y$ .

$2 x^{2} - 3 x y + y^{2}$

Factor $- 3$ out of $- 3 x y$ .

$2 x^{2} - 3 (x y) + y^{2}$

Rewrite $- 3$ as $- 1$ plus $- 2$

$2 x^{2} + (- 1 - 2) (x y) + y^{2}$

Apply the distributive property.

$2 x^{2} - 1 (x y) - 2 (x y) + y^{2}$

Remove unnecessary parentheses.

$2 x^{2} - 1 x y - 2 (x y) + y^{2}$

Remove unnecessary parentheses.

$2 x^{2} - 1 x y - 2 x y + y^{2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 1 x y) - 2 x y + y^{2}$

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

$x (2 x - 1 y) - y (2 x - y)$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1 y$ .

$(2 x - 1 y) (x - y)$

Step 2

Rewrite $- 1 y$ as $- y$ .

$(2 x - y) (x - y)$

Factor 2x^2-3xy+y^2

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