Factor n^2+18n+81

$n^{2} + 18 n + 81$

Step 1

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

$n^{2} + 18 n + 9^{2}$

Step 2

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

$18 n = 2 \cdot n \cdot 9$

Step 3

Rewrite the polynomial.

$n^{2} + 2 \cdot n \cdot 9 + 9^{2}$

Step 4

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

${(n + 9)}^{2}$