Algebra Examples

z^{2} - 2 z + 1

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

Step 1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

z^{2} - 2 z + 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

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

Step 3

Rewrite the polynomial.

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

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

Step 4

Factor using the perfect square trinomial rule

a^{2} - 2 a b + b^{2} = {(a - b)}^{2}

$a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where

a = z

$a = z$ and

b = 1

$b = 1$ .

{(z - 1)}^{2}

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