Factor 1+y^2-2y

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

Rearrange terms.

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

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

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

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

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

Rewrite the polynomial.

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

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

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