Basic Math Examples

$\frac{y^{2}}{y - 3} \cdot y^{2} - y - 6$

Step 1

Multiply $\frac{y^{2}}{y - 3} y^{2}$ .

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Step 1.1

Combine $\frac{y^{2}}{y - 3}$ and $y^{2}$ .

$\frac{y^{2} y^{2}}{y - 3} - y - 6$

Step 1.2

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

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Step 1.2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{y^{2 + 2}}{y - 3} - y - 6$

Step 1.2.2

Add $2$ and $2$ .

$\frac{y^{4}}{y - 3} - y - 6$

Step 2

Find the common denominator.

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Step 2.1

Write $- y$ as a fraction with denominator $1$ .

$\frac{y^{4}}{y - 3} + \frac{- y}{1} - 6$

Step 2.2

Multiply $\frac{- y}{1}$ by $\frac{y - 3}{y - 3}$ .

$\frac{y^{4}}{y - 3} + \frac{- y}{1} \cdot \frac{y - 3}{y - 3} - 6$

Step 2.3

Multiply $\frac{- y}{1}$ by $\frac{y - 3}{y - 3}$ .

$\frac{y^{4}}{y - 3} + \frac{- y (y - 3)}{y - 3} - 6$

Step 2.4

Write $- 6$ as a fraction with denominator $1$ .

$\frac{y^{4}}{y - 3} + \frac{- y (y - 3)}{y - 3} + \frac{- 6}{1}$

Step 2.5

Multiply $\frac{- 6}{1}$ by $\frac{y - 3}{y - 3}$ .

$\frac{y^{4}}{y - 3} + \frac{- y (y - 3)}{y - 3} + \frac{- 6}{1} \cdot \frac{y - 3}{y - 3}$

Step 2.6

Multiply $\frac{- 6}{1}$ by $\frac{y - 3}{y - 3}$ .

$\frac{y^{4}}{y - 3} + \frac{- y (y - 3)}{y - 3} + \frac{- 6 (y - 3)}{y - 3}$

Step 3

Combine the numerators over the common denominator.

$\frac{y^{4} - y (y - 3) - 6 (y - 3)}{y - 3}$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$\frac{y^{4} - y \cdot y - y \cdot - 3 - 6 (y - 3)}{y - 3}$

Step 4.2

Multiply $y$ by $y$ by adding the exponents.

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Step 4.2.1

Move $y$ .

$\frac{y^{4} - (y \cdot y) - y \cdot - 3 - 6 (y - 3)}{y - 3}$

Step 4.2.2

Multiply $y$ by $y$ .

$\frac{y^{4} - y^{2} - y \cdot - 3 - 6 (y - 3)}{y - 3}$

Step 4.3

Multiply $- 3$ by $- 1$ .

$\frac{y^{4} - y^{2} + 3 y - 6 (y - 3)}{y - 3}$

Step 4.4

Apply the distributive property.

$\frac{y^{4} - y^{2} + 3 y - 6 y - 6 \cdot - 3}{y - 3}$

Step 4.5

Multiply $- 6$ by $- 3$ .

$\frac{y^{4} - y^{2} + 3 y - 6 y + 18}{y - 3}$

Step 5

Subtract $6 y$ from $3 y$ .

$\frac{y^{4} - y^{2} - 3 y + 18}{y - 3}$