Solve 3m^3+12m^2+9m

$$3 m ^ { 3 } + 12 m ^ { 2 } + 9 m$$

Factor

$$3m\left(m+1\right)\left(m+3\right)$$

Solution Steps

Factor out 3.

$$3\left(m^{3}+4m^{2}+3m\right)$$

Consider m^{3}+4m^{2}+3m. Factor out m.

$$m\left(m^{2}+4m+3\right)$$

Consider m^{2}+4m+3. Factor the expression by grouping. First, the expression needs to be rewritten as m^{2}+am+bm+3. To find a and b, set up a system to be solved.

$$a+b=4 ab=1\times 3=3$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.

$$a=1 b=3$$

Rewrite m^{2}+4m+3 as \left(m^{2}+m\right)+\left(3m+3\right).

$$\left(m^{2}+m\right)+\left(3m+3\right)$$

Factor out m in the first and 3 in the second group.

$$m\left(m+1\right)+3\left(m+1\right)$$

Factor out common term m+1 by using distributive property.

$$\left(m+1\right)\left(m+3\right)$$

Rewrite the complete factored expression.

$$3m\left(m+1\right)\left(m+3\right)$$

Evaluate

$$3m\left(m+1\right)\left(m+3\right)$$