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

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

Solve for m

$$m<3$$

Solution Steps

Use the distributive property to multiply -2 by m-1.

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

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

$$4m^{2}-8m+4-4\left(m-2\right)\left(m+1\right)>0$$

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

$$4m^{2}-8m+4+\left(-4m+8\right)\left(m+1\right)>0$$

Use the distributive property to multiply -4m+8 by m+1 and combine like terms.

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

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

$$-8m+4+4m+8>0$$

Combine -8m and 4m to get -4m.

$$-4m+4+8>0$$

Add 4 and 8 to get 12.

$$-4m+12>0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-4m>-12$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$m<\frac{-12}{-4}$$

Divide -12 by -4 to get 3.

$$m<3$$