Factor m^3+6m^2+9m

$m^{3} + 6 m^{2} + 9 m$

Step 1

Factor $m$ out of $m^{3} + 6 m^{2} + 9 m$ .

Factor $m$ out of $m^{3}$ .

$m \cdot m^{2} + 6 m^{2} + 9 m$

Factor $m$ out of $6 m^{2}$ .

$m \cdot m^{2} + m (6 m) + 9 m$

Factor $m$ out of $9 m$ .

$m \cdot m^{2} + m (6 m) + m \cdot 9$

Factor $m$ out of $m \cdot m^{2} + m (6 m)$ .

$m (m^{2} + 6 m) + m \cdot 9$

Factor $m$ out of $m (m^{2} + 6 m) + m \cdot 9$ .

$m (m^{2} + 6 m + 9)$

Step 2

Factor using the perfect square rule.

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

$m (m^{2} + 6 m + 3^{2})$

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

$6 m = 2 \cdot m \cdot 3$

Rewrite the polynomial.

$m (m^{2} + 2 \cdot m \cdot 3 + 3^{2})$

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

$m {(m + 3)}^{2}$