Factor v^2-18v+81

$v^{2} - 18 v + 81$

Step 1

Rewrite $81$ as $9^{2}$ .

$v^{2} - 18 v + 9^{2}$

Step 2

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

$18 v = 2 \cdot v \cdot 9$

Step 3

Rewrite the polynomial.

$v^{2} - 2 \cdot v \cdot 9 + 9^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = v$ and $b = 9$ .

${(v - 9)}^{2}$