Factor y^2+2y+1

$y^{2} + 2 y + 1$

Step 1

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

$y^{2} + 2 y + 1^{2}$

Step 2

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

$2 y = 2 \cdot y \cdot 1$

Step 3

Rewrite the polynomial.

$y^{2} + 2 \cdot y \cdot 1 + 1^{2}$

Step 4

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

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