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

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

Evaluate

Solution Steps

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

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

Remove the parentheses around m.

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

Use the distributive property to multiply -4m by m-1.

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

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

$$1-4m+4m<0$$

Combine -4m and 4m to get 0.

$$1<0$$

Compare 1 and 0.

$$\text{false}$$