Factor 9h^2+60h+100

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

Step 1

Rewrite $9 h^{2}$ as ${(3 h)}^{2}$ .

${(3 h)}^{2} + 60 h + 100$

Step 2

Rewrite $100$ as $10^{2}$ .

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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