Factor x^2+30x+225

$x^{2} + 30 x + 225$

Step 1

Rewrite $225$ as $15^{2}$ .

$x^{2} + 30 x + 15^{2}$

Step 2

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

$30 x = 2 \cdot x \cdot 15$

Step 3

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot 15 + 15^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 15$ .

${(x + 15)}^{2}$