Solve g(t)=(7+1/t)(t^4-1/8)

$$g ( t ) = ( 7 + \frac { 1 } { t } ) ( t ^ { 4 } - \frac { 1 } { 8 } )$$

Evaluate

$$7t^{4}+t^{3}-\frac{7}{8}-\frac{1}{8t}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{t}{t}.

$$\left(\frac{7t}{t}+\frac{1}{t}\right)\left(t^{4}-\frac{1}{8}\right)$$

Since \frac{7t}{t} and \frac{1}{t} have the same denominator, add them by adding their numerators.

$$\frac{7t+1}{t}\left(t^{4}-\frac{1}{8}\right)$$

Use the distributive property to multiply \frac{7t+1}{t} by t^{4}-\frac{1}{8}.

$$\frac{7t+1}{t}t^{4}-\frac{1}{8}\times \frac{7t+1}{t}$$

Express \frac{7t+1}{t}t^{4} as a single fraction.

$$\frac{\left(7t+1\right)t^{4}}{t}-\frac{1}{8}\times \frac{7t+1}{t}$$

Cancel out t in both numerator and denominator.

$$\left(7t+1\right)t^{3}-\frac{1}{8}\times \frac{7t+1}{t}$$

Use the distributive property to multiply 7t+1 by t^{3}.

$$7t^{4}+t^{3}-\frac{1}{8}\times \frac{7t+1}{t}$$

Multiply -\frac{1}{8} times \frac{7t+1}{t} by multiplying numerator times numerator and denominator times denominator.

$$7t^{4}+t^{3}+\frac{-\left(7t+1\right)}{8t}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7t^{4}+t^{3} times \frac{8t}{8t}.

$$\frac{\left(7t^{4}+t^{3}\right)\times 8t}{8t}+\frac{-\left(7t+1\right)}{8t}$$

Since \frac{\left(7t^{4}+t^{3}\right)\times 8t}{8t} and \frac{-\left(7t+1\right)}{8t} have the same denominator, add them by adding their numerators.

$$\frac{\left(7t^{4}+t^{3}\right)\times 8t-\left(7t+1\right)}{8t}$$

Do the multiplications in \left(7t^{4}+t^{3}\right)\times 8t-\left(7t+1\right).

$$\frac{56t^{5}+8t^{4}-7t-1}{8t}$$

Expand

$$7t^{4}+t^{3}-\frac{7}{8}-\frac{1}{8t}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{t}{t}.

$$\left(\frac{7t}{t}+\frac{1}{t}\right)\left(t^{4}-\frac{1}{8}\right)$$

Since \frac{7t}{t} and \frac{1}{t} have the same denominator, add them by adding their numerators.

$$\frac{7t+1}{t}\left(t^{4}-\frac{1}{8}\right)$$

Use the distributive property to multiply \frac{7t+1}{t} by t^{4}-\frac{1}{8}.

$$\frac{7t+1}{t}t^{4}-\frac{1}{8}\times \frac{7t+1}{t}$$

Express \frac{7t+1}{t}t^{4} as a single fraction.

$$\frac{\left(7t+1\right)t^{4}}{t}-\frac{1}{8}\times \frac{7t+1}{t}$$

Cancel out t in both numerator and denominator.

$$\left(7t+1\right)t^{3}-\frac{1}{8}\times \frac{7t+1}{t}$$

Use the distributive property to multiply 7t+1 by t^{3}.

$$7t^{4}+t^{3}-\frac{1}{8}\times \frac{7t+1}{t}$$

Multiply -\frac{1}{8} times \frac{7t+1}{t} by multiplying numerator times numerator and denominator times denominator.

$$7t^{4}+t^{3}+\frac{-\left(7t+1\right)}{8t}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7t^{4}+t^{3} times \frac{8t}{8t}.

$$\frac{\left(7t^{4}+t^{3}\right)\times 8t}{8t}+\frac{-\left(7t+1\right)}{8t}$$

Since \frac{\left(7t^{4}+t^{3}\right)\times 8t}{8t} and \frac{-\left(7t+1\right)}{8t} have the same denominator, add them by adding their numerators.

$$\frac{\left(7t^{4}+t^{3}\right)\times 8t-\left(7t+1\right)}{8t}$$

Do the multiplications in \left(7t^{4}+t^{3}\right)\times 8t-\left(7t+1\right).

$$\frac{56t^{5}+8t^{4}-7t-1}{8t}$$