Factor 25x^2+30x+9

$25 x^{2} + 30 x + 9$

Step 1

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

${(5 x)}^{2} + 30 x + 9$

Step 2

Rewrite $9$ as $3^{2}$ .

${(5 x)}^{2} + 30 x + 3^{2}$

Step 3

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

$30 x = 2 \cdot (5 x) \cdot 3$

Step 4

Rewrite the polynomial.

${(5 x)}^{2} + 2 \cdot (5 x) \cdot 3 + 3^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 5 x$ and $b = 3$ .

${(5 x + 3)}^{2}$