Solve (-t/2)^2+t*(-t/2)+2

$$( - \frac { t } { 2 } ) ^ { 2 } + t \cdot ( - \frac { t } { 2 } ) + 2$$

Evaluate

$$-\frac{t^{2}}{4}+2$$

Short Solution Steps

Calculate -\frac{t}{2} to the power of 2 and get \left(\frac{t}{2}\right)^{2}.

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

Express t\left(-\frac{t}{2}\right) as a single fraction.

$$\left(\frac{t}{2}\right)^{2}+\frac{-tt}{2}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2}{2}.

$$\left(\frac{t}{2}\right)^{2}+\frac{-tt}{2}+\frac{2\times 2}{2}$$

Since \frac{-tt}{2} and \frac{2\times 2}{2} have the same denominator, add them by adding their numerators.

$$\left(\frac{t}{2}\right)^{2}+\frac{-tt+2\times 2}{2}$$

Do the multiplications in -tt+2\times 2.

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

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

$$\frac{t^{2}}{2^{2}}+\frac{-t^{2}+4}{2}$$

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{-t^{2}+4}{2} times \frac{2}{2}.

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

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

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

Do the multiplications in t^{2}+2\left(-t^{2}+4\right).

$$\frac{t^{2}-2t^{2}+8}{4}$$

Combine like terms in t^{2}-2t^{2}+8.

$$\frac{-t^{2}+8}{4}$$

Expand

$$-\frac{t^{2}}{4}+2$$

Short Solution Steps

Calculate -\frac{t}{2} to the power of 2 and get \left(\frac{t}{2}\right)^{2}.

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

Express t\left(-\frac{t}{2}\right) as a single fraction.

$$\left(\frac{t}{2}\right)^{2}+\frac{-tt}{2}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2}{2}.

$$\left(\frac{t}{2}\right)^{2}+\frac{-tt}{2}+\frac{2\times 2}{2}$$

Since \frac{-tt}{2} and \frac{2\times 2}{2} have the same denominator, add them by adding their numerators.

$$\left(\frac{t}{2}\right)^{2}+\frac{-tt+2\times 2}{2}$$

Do the multiplications in -tt+2\times 2.

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

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

$$\frac{t^{2}}{2^{2}}+\frac{-t^{2}+4}{2}$$

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{-t^{2}+4}{2} times \frac{2}{2}.

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

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

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

Do the multiplications in t^{2}+2\left(-t^{2}+4\right).

$$\frac{t^{2}-2t^{2}+8}{4}$$

Combine like terms in t^{2}-2t^{2}+8.

$$\frac{-t^{2}+8}{4}$$