Factor d^2+18d+81

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

Step 1

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

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

Step 2

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

$18 d = 2 \cdot d \cdot 9$

Step 3

Rewrite the polynomial.

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

Step 4

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

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