Factor z^2-14z+49

$z^{2} - 14 z + 49$

Step 1

Rewrite $49$ as $7^{2}$ .

$z^{2} - 14 z + 7^{2}$

Step 2

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

$14 z = 2 \cdot z \cdot 7$

Step 3

Rewrite the polynomial.

$z^{2} - 2 \cdot z \cdot 7 + 7^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = z$ and $b = 7$ .

${(z - 7)}^{2}$