Solve 1-t^2/2+1/5-1/25

$$\frac{ 1- { t }^{ 2 } }{ 2 } + \frac{ 1 }{ 5 } - \frac{ 1 }{ 25 }$$

Evaluate

$$-\frac{t^{2}}{2}+\frac{33}{50}$$

Short Solution Steps

Subtract \frac{1}{25} from \frac{1}{5} to get \frac{4}{25}.

$$\frac{1-t^{2}}{2}+\frac{4}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 25 is 50. Multiply \frac{1-t^{2}}{2} times \frac{25}{25}. Multiply \frac{4}{25} times \frac{2}{2}.

$$\frac{25\left(1-t^{2}\right)}{50}+\frac{4\times 2}{50}$$

Since \frac{25\left(1-t^{2}\right)}{50} and \frac{4\times 2}{50} have the same denominator, add them by adding their numerators.

$$\frac{25\left(1-t^{2}\right)+4\times 2}{50}$$

Do the multiplications in 25\left(1-t^{2}\right)+4\times 2.

$$\frac{25-25t^{2}+8}{50}$$

Combine like terms in 25-25t^{2}+8.

$$\frac{33-25t^{2}}{50}$$

Expand

$$-\frac{t^{2}}{2}+\frac{33}{50}$$

Short Solution Steps

Subtract \frac{1}{25} from \frac{1}{5} to get \frac{4}{25}.

$$\frac{1-t^{2}}{2}+\frac{4}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 25 is 50. Multiply \frac{1-t^{2}}{2} times \frac{25}{25}. Multiply \frac{4}{25} times \frac{2}{2}.

$$\frac{25\left(1-t^{2}\right)}{50}+\frac{4\times 2}{50}$$

Since \frac{25\left(1-t^{2}\right)}{50} and \frac{4\times 2}{50} have the same denominator, add them by adding their numerators.

$$\frac{25\left(1-t^{2}\right)+4\times 2}{50}$$

Do the multiplications in 25\left(1-t^{2}\right)+4\times 2.

$$\frac{25-25t^{2}+8}{50}$$

Combine like terms in 25-25t^{2}+8.

$$\frac{33-25t^{2}}{50}$$