Solve (m+2)^2-4(m+2)<0

$$( m + 2 ) ^ { 2 } - 4 ( m + 2 ) < 0$$

Solve for m

$$m\in \left(-2,2\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+2\right)^{2}.

$$m^{2}+4m+4-4\left(m+2\right)<0$$

Use the distributive property to multiply -4 by m+2.

$$m^{2}+4m+4-4m-8<0$$

Combine 4m and -4m to get 0.

$$m^{2}+4-8<0$$

Subtract 8 from 4 to get -4.

$$m^{2}-4<0$$

Add 4 to both sides.

$$m^{2}<4$$

Calculate the square root of 4 and get 2. Rewrite 4 as 2^{2}.

$$m^{2}<2^{2}$$

Inequality holds for |m|<2.

$$|m|<2$$

Rewrite |m|<2 as m\in \left(-2,2\right).

$$m\in \left(-2,2\right)$$