Factor r^2+24r+144

$r^{2} + 24 r + 144$

Step 1

Rewrite $144$ as $12^{2}$ .

$r^{2} + 24 r + 12^{2}$

Step 2

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

$24 r = 2 \cdot r \cdot 12$

Step 3

Rewrite the polynomial.

$r^{2} + 2 \cdot r \cdot 12 + 12^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = r$ and $b = 12$ .

${(r + 12)}^{2}$