Solve (m+1)^2-m(m-2)>0

$$( m + 1 ) ^ { 2 } - m ( m - 2 ) > 0$$

Solve for m

$$m>-\frac{1}{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+1\right)^{2}.

$$m^{2}+2m+1-m\left(m-2\right)>0$$

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

$$m^{2}+2m+1-\left(m^{2}-2m\right)>0$$

To find the opposite of m^{2}-2m, find the opposite of each term.

$$m^{2}+2m+1-m^{2}+2m>0$$

Combine m^{2} and -m^{2} to get 0.

$$2m+1+2m>0$$

Combine 2m and 2m to get 4m.

$$4m+1>0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$4m>-1$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$m>-\frac{1}{4}$$