Factor 81x^2+36x+4

$81 x^{2} + 36 x + 4$

Step 1

Rewrite $81 x^{2}$ as ${(9 x)}^{2}$ .

${(9 x)}^{2} + 36 x + 4$

Step 2

Rewrite $4$ as $2^{2}$ .

${(9 x)}^{2} + 36 x + 2^{2}$

Step 3

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

$36 x = 2 \cdot (9 x) \cdot 2$

Step 4

Rewrite the polynomial.

${(9 x)}^{2} + 2 \cdot (9 x) \cdot 2 + 2^{2}$

Step 5

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

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