Factor 100x^2+60x+9

$100 x^{2} + 60 x + 9$

Step 1

Rewrite $100 x^{2}$ as ${(10 x)}^{2}$ .

${(10 x)}^{2} + 60 x + 9$

Step 2

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

${(10 x)}^{2} + 60 x + 3^{2}$

Step 3

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

$60 x = 2 \cdot (10 x) \cdot 3$

Step 4

Rewrite the polynomial.

${(10 x)}^{2} + 2 \cdot (10 x) \cdot 3 + 3^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 10 x$ and $b = 3$ .

${(10 x + 3)}^{2}$