Factor v^2-6v+9

$v^{2} - 6 v + 9$

Step 1

Rewrite $9$ as $3^{2}$ .

$v^{2} - 6 v + 3^{2}$

Step 2

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

$6 v = 2 \cdot v \cdot 3$

Step 3

Rewrite the polynomial.

$v^{2} - 2 \cdot v \cdot 3 + 3^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = v$ and $b = 3$ .

${(v - 3)}^{2}$