Precalculus Examples

$4 z^{2} - 4 z + 1$

Step 1

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

${(2 z)}^{2} - 4 z + 1$

Step 2

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

${(2 z)}^{2} - 4 z + 1^{2}$

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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