Basic Math Examples

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

Step 1

Factor $2$ out of $2 a^{2} + 4 a b + 2 b^{2}$ .

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Step 1.1

Factor $2$ out of $2 a^{2}$ .

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

Step 1.2

Factor $2$ out of $4 a b$ .

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

Step 1.3

Factor $2$ out of $2 b^{2}$ .

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

Step 1.4

Factor $2$ out of $2 (a^{2}) + 2 (2 a b)$ .

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

Step 1.5

Factor $2$ out of $2 (a^{2} + 2 a b) + 2 (b^{2})$ .

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

Step 2

Factor using the perfect square rule.

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Step 2.1

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 a b = 2 \cdot a \cdot b$

Step 2.2

Rewrite the polynomial.

$2 (a^{2} + 2 \cdot a \cdot b + b^{2})$

Step 2.3

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = a$ and $b = b$ .

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