Basic Math Examples

$\frac{36 y^{7} - 12 y^{4}}{4 y^{3}}$

Step 1

Simplify terms.

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Step 1.1

Factor $12 y^{4}$ out of $36 y^{7} - 12 y^{4}$ .

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Step 1.1.1

Factor $12 y^{4}$ out of $36 y^{7}$ .

$\frac{12 y^{4} (3 y^{3}) - 12 y^{4}}{4 y^{3}}$

Step 1.1.2

Factor $12 y^{4}$ out of $- 12 y^{4}$ .

$\frac{12 y^{4} (3 y^{3}) + 12 y^{4} (- 1)}{4 y^{3}}$

Step 1.1.3

Factor $12 y^{4}$ out of $12 y^{4} (3 y^{3}) + 12 y^{4} (- 1)$ .

$\frac{12 y^{4} (3 y^{3} - 1)}{4 y^{3}}$

Step 1.2

Cancel the common factor of $12$ and $4$ .

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Step 1.2.1

Factor $4$ out of $12 y^{4} (3 y^{3} - 1)$ .

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $4$ out of $4 y^{3}$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 1.3

Cancel the common factor of $y^{4}$ and $y^{3}$ .

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Step 1.3.1

Factor $y^{3}$ out of $3 y^{4} (3 y^{3} - 1)$ .

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

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Multiply by $1$ .

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

Step 1.3.2.2

Cancel the common factor.

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

Step 1.3.2.3

Rewrite the expression.

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

Step 1.3.2.4

Divide $3 y (3 y^{3} - 1)$ by $1$ .

$3 y (3 y^{3} - 1)$

Step 1.4

Apply the distributive property.

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

Step 1.5

Simplify the expression.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 y \cdot y^{3} + 3 y \cdot - 1$

Step 1.5.2

Multiply $- 1$ by $3$ .

$3 \cdot 3 y \cdot y^{3} - 3 y$

Step 2

Simplify each term.

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Step 2.1

Multiply $y$ by $y^{3}$ by adding the exponents.

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Step 2.1.1

Move $y^{3}$ .

$3 \cdot 3 (y^{3} y) - 3 y$

Step 2.1.2

Multiply $y^{3}$ by $y$ .

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Step 2.1.2.1

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

$3 \cdot 3 (y^{3} y^{1}) - 3 y$

Step 2.1.2.2

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

$3 \cdot 3 y^{3 + 1} - 3 y$

Step 2.1.3

Add $3$ and $1$ .

$3 \cdot 3 y^{4} - 3 y$

Step 2.2

Multiply $3$ by $3$ .

$9 y^{4} - 3 y$