Solve (-m-1/2)^2+m(-m-1)/2

$$( \frac { - m - 1 } { 2 } ) ^ { 2 } + \frac { m ( - m - 1 ) } { 2 }$$

Evaluate

$$\frac{1-m^{2}}{4}$$

Short Solution Steps

To raise \frac{-m-1}{2} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2^{2} and 2 is 4. Multiply \frac{m\left(-m\right)-m}{2} times \frac{2}{2}.

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

Since \frac{\left(-m-1\right)^{2}}{4} and \frac{2\left(m\left(-m\right)-m\right)}{4} have the same denominator, add them by adding their numerators.

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

Multiply m and m to get m^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{m^{2}\left(-1\right)-m}{2} times \frac{2}{2}.

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

Since \frac{\left(-m-1\right)^{2}}{4} and \frac{2\left(m^{2}\left(-1\right)-m\right)}{4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(-m-1\right)^{2}+2\left(m^{2}\left(-1\right)-m\right).

$$\frac{m^{2}+2m+1-2m^{2}-2m}{4}$$

Combine like terms in m^{2}+2m+1-2m^{2}-2m.

$$\frac{-m^{2}+1}{4}$$

Expand

$$\frac{1-m^{2}}{4}$$

Short Solution Steps

To raise \frac{-m-1}{2} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2^{2} and 2 is 4. Multiply \frac{m\left(-m\right)-m}{2} times \frac{2}{2}.

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

Since \frac{\left(-m-1\right)^{2}}{4} and \frac{2\left(m\left(-m\right)-m\right)}{4} have the same denominator, add them by adding their numerators.

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

Multiply m and m to get m^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{m^{2}\left(-1\right)-m}{2} times \frac{2}{2}.

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

Since \frac{\left(-m-1\right)^{2}}{4} and \frac{2\left(m^{2}\left(-1\right)-m\right)}{4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(-m-1\right)^{2}+2\left(m^{2}\left(-1\right)-m\right).

$$\frac{m^{2}+2m+1-2m^{2}-2m}{4}$$

Combine like terms in m^{2}+2m+1-2m^{2}-2m.

$$\frac{-m^{2}+1}{4}$$