Solve =(3+1/t)(t^3-1/7)

$$= ( 3 + \frac { 1 } { t } ) ( t ^ { 3 } - \frac { 1 } { 7 } )$$

Evaluate

$$3t^{3}+t^{2}-\frac{3}{7}-\frac{1}{7t}$$

Short Solution Steps

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

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

Since \frac{3t}{t} and \frac{1}{t} have the same denominator, add them by adding their numerators.

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

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

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

Express \frac{3t+1}{t}t^{3} as a single fraction.

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

Cancel out t in both numerator and denominator.

$$\left(3t+1\right)t^{2}-\frac{1}{7}\times \frac{3t+1}{t}$$

Use the distributive property to multiply 3t+1 by t^{2}.

$$3t^{3}+t^{2}-\frac{1}{7}\times \frac{3t+1}{t}$$

Multiply -\frac{1}{7} times \frac{3t+1}{t} by multiplying numerator times numerator and denominator times denominator.

$$3t^{3}+t^{2}+\frac{-\left(3t+1\right)}{7t}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3t^{3}+t^{2} times \frac{7t}{7t}.

$$\frac{\left(3t^{3}+t^{2}\right)\times 7t}{7t}+\frac{-\left(3t+1\right)}{7t}$$

Since \frac{\left(3t^{3}+t^{2}\right)\times 7t}{7t} and \frac{-\left(3t+1\right)}{7t} have the same denominator, add them by adding their numerators.

$$\frac{\left(3t^{3}+t^{2}\right)\times 7t-\left(3t+1\right)}{7t}$$

Do the multiplications in \left(3t^{3}+t^{2}\right)\times 7t-\left(3t+1\right).

$$\frac{21t^{4}+7t^{3}-3t-1}{7t}$$

Expand

$$3t^{3}+t^{2}-\frac{3}{7}-\frac{1}{7t}$$

Short Solution Steps

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

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

Since \frac{3t}{t} and \frac{1}{t} have the same denominator, add them by adding their numerators.

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

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

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

Express \frac{3t+1}{t}t^{3} as a single fraction.

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

Cancel out t in both numerator and denominator.

$$\left(3t+1\right)t^{2}-\frac{1}{7}\times \frac{3t+1}{t}$$

Use the distributive property to multiply 3t+1 by t^{2}.

$$3t^{3}+t^{2}-\frac{1}{7}\times \frac{3t+1}{t}$$

Multiply -\frac{1}{7} times \frac{3t+1}{t} by multiplying numerator times numerator and denominator times denominator.

$$3t^{3}+t^{2}+\frac{-\left(3t+1\right)}{7t}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3t^{3}+t^{2} times \frac{7t}{7t}.

$$\frac{\left(3t^{3}+t^{2}\right)\times 7t}{7t}+\frac{-\left(3t+1\right)}{7t}$$

Since \frac{\left(3t^{3}+t^{2}\right)\times 7t}{7t} and \frac{-\left(3t+1\right)}{7t} have the same denominator, add them by adding their numerators.

$$\frac{\left(3t^{3}+t^{2}\right)\times 7t-\left(3t+1\right)}{7t}$$

Do the multiplications in \left(3t^{3}+t^{2}\right)\times 7t-\left(3t+1\right).

$$\frac{21t^{4}+7t^{3}-3t-1}{7t}$$