# How do you factor x^2+18x+81?

Jun 1, 2016

${x}^{2} + 18 x + 81 = {\left(x + 9\right)}^{2}$

#### Explanation:

As $81$ is the square of $9$ and middle term $18$ is double of this number, (compare it with ${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$)

Hence ${x}^{2} + 18 x + 81$ is a complete square.

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

= ${x}^{2} + 2 \times 9 \times x + {9}^{2}$

= ${\left(x + 9\right)}^{2}$