Factor 3+6b+3b^2

$3 + 6 b + 3 b^{2}$

Step 1

Factor $3$ out of $3 + 6 b + 3 b^{2}$ .

Factor $3$ out of $3$ .

$3 \cdot 1 + 6 b + 3 b^{2}$

Factor $3$ out of $6 b$ .

$3 \cdot 1 + 3 (2 b) + 3 b^{2}$

Factor $3$ out of $3 \cdot 1 + 3 (2 b)$ .

$3 \cdot (1 + 2 b) + 3 b^{2}$

Factor $3$ out of $3 \cdot (1 + 2 b) + 3 b^{2}$ .

$3 (1 + 2 b + b^{2})$

Step 2

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$3 (1^{2} + 2 b + b^{2})$

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

$2 b = 2 \cdot 1 \cdot b$

Rewrite the polynomial.

$3 (1^{2} + 2 \cdot 1 \cdot b + b^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 1$ and $b = b$ .

$3 {(1 + b)}^{2}$