Factor 4b^2+4b+1

$4 b^{2} + 4 b + 1$

Step 1

Rewrite $4 b^{2}$ as ${(2 b)}^{2}$ .

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

Step 2

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

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

Step 3

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

$4 b = 2 \cdot (2 b) \cdot 1$

Step 4

Rewrite the polynomial.

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

Step 5

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

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