Factor 2x^2+5xy+2y^2

$2 x^{2} + 5 x y + 2 y^{2}$

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 $a \cdot c = 2 \cdot 2 = 4$ and whose sum is $b = 5$ .

Reorder terms.

$2 x^{2} + 2 y^{2} + 5 x y$

Reorder $2 y^{2}$ and $5 x y$ .

$2 x^{2} + 5 x y + 2 y^{2}$

Factor $5$ out of $5 x y$ .

$2 x^{2} + 5 (x y) + 2 y^{2}$

Rewrite $5$ as $1$ plus $4$

$2 x^{2} + (1 + 4) (x y) + 2 y^{2}$

Apply the distributive property.

$2 x^{2} + 1 (x y) + 4 (x y) + 2 y^{2}$

Multiply $x y$ by $1$ .

$2 x^{2} + x y + 4 (x y) + 2 y^{2}$

Remove unnecessary parentheses.

$2 x^{2} + x y + 4 x y + 2 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + x y) + 4 x y + 2 y^{2}$

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

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

Step 3

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

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

Factor 2x^2+5xy+2y^2

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