Factor z^2-2z+1

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

Step 1

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

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

Step 2

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

$2 z = 2 \cdot z \cdot 1$

Step 3

Rewrite the polynomial.

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

Step 4

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

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