Solve left(3y-1/yright)y^4/3

$$\left( 3y- \frac{ 1 }{ y } \right) \frac{ { y }^{ 4 } }{ 3 }$$

Evaluate

$$y^{5}-\frac{y^{3}}{3}$$

Short Solution Steps

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

$$\left(\frac{3yy}{y}-\frac{1}{y}\right)\times \frac{y^{4}}{3}$$

Since \frac{3yy}{y} and \frac{1}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3yy-1}{y}\times \frac{y^{4}}{3}$$

Do the multiplications in 3yy-1.

$$\frac{3y^{2}-1}{y}\times \frac{y^{4}}{3}$$

Multiply \frac{3y^{2}-1}{y} times \frac{y^{4}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3y^{2}-1\right)y^{4}}{y\times 3}$$

Cancel out y in both numerator and denominator.

$$\frac{\left(3y^{2}-1\right)y^{3}}{3}$$

Use the distributive property to multiply 3y^{2}-1 by y^{3}.

$$\frac{3y^{5}-y^{3}}{3}$$

Expand

$$y^{5}-\frac{y^{3}}{3}$$

Short Solution Steps

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

$$\left(\frac{3yy}{y}-\frac{1}{y}\right)\times \frac{y^{4}}{3}$$

Since \frac{3yy}{y} and \frac{1}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3yy-1}{y}\times \frac{y^{4}}{3}$$

Do the multiplications in 3yy-1.

$$\frac{3y^{2}-1}{y}\times \frac{y^{4}}{3}$$

Multiply \frac{3y^{2}-1}{y} times \frac{y^{4}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3y^{2}-1\right)y^{4}}{y\times 3}$$

Cancel out y in both numerator and denominator.

$$\frac{\left(3y^{2}-1\right)y^{3}}{3}$$

Use the distributive property to multiply 3y^{2}-1 by y^{3}.

$$\frac{3y^{5}-y^{3}}{3}$$