Solve (2m+1)^2-4(m^2-1)>0

$$( 2 m + 1 ) ^ { 2 } - 4 ( m ^ { 2 } - 1 ) > 0$$

Solve for m

$$m>-\frac{5}{4}$$

Solution Steps

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

$$4m^{2}+4m+1-4\left(m^{2}-1\right)>0$$

Use the distributive property to multiply -4 by m^{2}-1.

$$4m^{2}+4m+1-4m^{2}+4>0$$

Combine 4m^{2} and -4m^{2} to get 0.

$$4m+1+4>0$$

Add 1 and 4 to get 5.

$$4m+5>0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$4m>-5$$

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

$$m>-\frac{5}{4}$$