Basic Math Examples

$y - 2 \div 3 y^{2} - 4 y + 1$

Step 1

Rewrite the division as a fraction.

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

Step 2

To write $y$ as a fraction with a common denominator, multiply by $\frac{3 y^{2}}{3 y^{2}}$ .

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

Step 3

Simplify terms.

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Step 3.1

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

$\frac{y (3 y^{2})}{3 y^{2}} - \frac{2}{3 y^{2}} - 4 y + 1$

Step 3.2

Combine the numerators over the common denominator.

$\frac{y (3 y^{2}) - 2}{3 y^{2}} - 4 y + 1$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite using the commutative property of multiplication.

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

Step 4.2

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

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Step 4.2.1

Move $y^{2}$ .

$\frac{3 (y^{2} y) - 2}{3 y^{2}} - 4 y + 1$

Step 4.2.2

Multiply $y^{2}$ by $y$ .

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Step 4.2.2.1

Raise $y$ to the power of $1$ .

$\frac{3 (y^{2} y^{1}) - 2}{3 y^{2}} - 4 y + 1$

Step 4.2.2.2

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

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

Step 4.2.3

Add $2$ and $1$ .

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

Step 5

To write $- 4 y$ as a fraction with a common denominator, multiply by $\frac{3 y^{2}}{3 y^{2}}$ .

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

Step 6

Simplify terms.

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Step 6.1

Combine $- 4 y$ and $\frac{3 y^{2}}{3 y^{2}}$ .

$\frac{3 y^{3} - 2}{3 y^{2}} + \frac{- 4 y (3 y^{2})}{3 y^{2}} + 1$

Step 6.2

Combine the numerators over the common denominator.

$\frac{3 y^{3} - 2 - 4 y (3 y^{2})}{3 y^{2}} + 1$

Step 7

Simplify the numerator.

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Step 7.1

Rewrite using the commutative property of multiplication.

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

Step 7.2

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

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Step 7.2.1

Move $y^{2}$ .

$\frac{3 y^{3} - 2 - 4 \cdot 3 (y^{2} y)}{3 y^{2}} + 1$

Step 7.2.2

Multiply $y^{2}$ by $y$ .

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Step 7.2.2.1

Raise $y$ to the power of $1$ .

$\frac{3 y^{3} - 2 - 4 \cdot 3 (y^{2} y^{1})}{3 y^{2}} + 1$

Step 7.2.2.2

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

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

Step 7.2.3

Add $2$ and $1$ .

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

Step 7.3

Multiply $- 4$ by $3$ .

$\frac{3 y^{3} - 2 - 12 y^{3}}{3 y^{2}} + 1$

Step 7.4

Subtract $12 y^{3}$ from $3 y^{3}$ .

$\frac{- 9 y^{3} - 2}{3 y^{2}} + 1$

Step 8

Simplify terms.

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Step 8.1

Write $1$ as a fraction with a common denominator.

$\frac{- 9 y^{3} - 2}{3 y^{2}} + \frac{3 y^{2}}{3 y^{2}}$

Step 8.2

Combine the numerators over the common denominator.

$\frac{- 9 y^{3} - 2 + 3 y^{2}}{3 y^{2}}$

Step 8.3

Reorder terms.

$\frac{- 9 y^{3} + 3 y^{2} - 2}{3 y^{2}}$

Step 8.4

Factor $- 1$ out of $- 9 y^{3}$ .

$\frac{- (9 y^{3}) + 3 y^{2} - 2}{3 y^{2}}$

Step 8.5

Factor $- 1$ out of $3 y^{2}$ .

$\frac{- (9 y^{3}) - (- 3 y^{2}) - 2}{3 y^{2}}$

Step 8.6

Factor $- 1$ out of $- (9 y^{3}) - (- 3 y^{2})$ .

$\frac{- (9 y^{3} - 3 y^{2}) - 2}{3 y^{2}}$

Step 8.7

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- (9 y^{3} - 3 y^{2}) - 1 (2)}{3 y^{2}}$

Step 8.8

Factor $- 1$ out of $- (9 y^{3} - 3 y^{2}) - 1 (2)$ .

$\frac{- (9 y^{3} - 3 y^{2} + 2)}{3 y^{2}}$

Step 8.9

Simplify the expression.

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Step 8.9.1

Rewrite $- (9 y^{3} - 3 y^{2} + 2)$ as $- 1 (9 y^{3} - 3 y^{2} + 2)$ .

$\frac{- 1 (9 y^{3} - 3 y^{2} + 2)}{3 y^{2}}$

Step 8.9.2

Move the negative in front of the fraction.

$- \frac{9 y^{3} - 3 y^{2} + 2}{3 y^{2}}$