Factor 81+18j+j^2

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

Step 1

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

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

Step 2

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

$18 j = 2 \cdot 9 \cdot j$

Step 3

Rewrite the polynomial.

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

Step 4

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

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