Factor 5x^2+7xy+2y^2

$5 x^{2} + 7 x y + 2 y^{2}$

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 $a \cdot c = 5 \cdot 2 = 10$ and whose sum is $b = 7$ .

Reorder terms.

$5 x^{2} + 2 y^{2} + 7 x y$

Reorder $2 y^{2}$ and $7 x y$ .

$5 x^{2} + 7 x y + 2 y^{2}$

Factor $7$ out of $7 x y$ .

$5 x^{2} + 7 (x y) + 2 y^{2}$

Rewrite $7$ as $2$ plus $5$

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

Apply the distributive property.

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$x (5 x + 2 y) + y (5 x + 2 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 2 y$ .

$(5 x + 2 y) (x + y)$

Factor 5x^2+7xy+2y^2

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