Factor 2a^2+5ab+2b^2

$2 a^{2} + 5 a b + 2 b^{2}$

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.

$2 a^{2} + 2 b^{2} + 5 a b$

Reorder $2 b^{2}$ and $5 a b$ .

$2 a^{2} + 5 a b + 2 b^{2}$

Factor $5$ out of $5 a b$ .

$2 a^{2} + 5 (a b) + 2 b^{2}$

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

$2 a^{2} + (1 + 4) (a b) + 2 b^{2}$

Apply the distributive property.

$2 a^{2} + 1 (a b) + 4 (a b) + 2 b^{2}$

Multiply $a b$ by $1$ .

$2 a^{2} + a b + 4 (a b) + 2 b^{2}$

Remove unnecessary parentheses.

$2 a^{2} + a b + 4 a b + 2 b^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 a^{2} + a b) + 4 a b + 2 b^{2}$

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

$a (2 a + b) + 2 b (2 a + b)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 a + b$ .

$(2 a + b) (a + 2 b)$

Factor 2a^2+5ab+2b^2

Related Questions

Support LCMGCF.com by disabling your adblocker.