Pre-Algebra Examples

$(36 x y^{4} - 24 x^{3} y^{3} + 18 x^{3} y^{2}) \div 6 x y$

Step 1

Rewrite the division as a fraction.

$\frac{36 x y^{4} - 24 x^{3} y^{3} + 18 x^{3} y^{2}}{6 x y}$

Step 2

Factor $6 x y^{2}$ out of $36 x y^{4} - 24 x^{3} y^{3} + 18 x^{3} y^{2}$ .

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Step 2.1

Factor $6 x y^{2}$ out of $36 x y^{4}$ .

$\frac{6 x y^{2} (6 y^{2}) - 24 x^{3} y^{3} + 18 x^{3} y^{2}}{6 x y}$

Step 2.2

Factor $6 x y^{2}$ out of $- 24 x^{3} y^{3}$ .

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

Step 2.3

Factor $6 x y^{2}$ out of $18 x^{3} y^{2}$ .

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

Step 2.4

Factor $6 x y^{2}$ out of $6 x y^{2} (6 y^{2}) + 6 x y^{2} (- 4 x^{2} y)$ .

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

Step 2.5

Factor $6 x y^{2}$ out of $6 x y^{2} (6 y^{2} - 4 x^{2} y) + 6 x y^{2} (3 x^{2})$ .

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

Step 3

Cancel the common factor of $6$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Cancel the common factor of $y^{2}$ and $y$ .

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Step 5.1

Factor $y$ out of $y^{2} (6 y^{2} - 4 x^{2} y + 3 x^{2})$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{y (y (6 y^{2} - 4 x^{2} y + 3 x^{2}))}{y^{1}}$

Step 5.2.2

Factor $y$ out of $y^{1}$ .

$\frac{y (y (6 y^{2} - 4 x^{2} y + 3 x^{2}))}{y \cdot 1}$

Step 5.2.3

Cancel the common factor.

$\frac{y (y (6 y^{2} - 4 x^{2} y + 3 x^{2}))}{y \cdot 1}$

Step 5.2.4

Rewrite the expression.

$\frac{y (6 y^{2} - 4 x^{2} y + 3 x^{2})}{1}$

Step 5.2.5

Divide $y (6 y^{2} - 4 x^{2} y + 3 x^{2})$ by $1$ .

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

Step 6

Apply the distributive property.

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

Step 7

Simplify.

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Step 7.1

Rewrite using the commutative property of multiplication.

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

Step 7.2

Rewrite using the commutative property of multiplication.

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

Step 7.3

Rewrite using the commutative property of multiplication.

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

Step 8

Simplify each term.

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Step 8.1

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

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Step 8.1.1

Move $y^{2}$ .

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

Step 8.1.2

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

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Step 8.1.2.1

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

$6 (y^{2} y^{1}) - 4 y (x^{2} y) + 3 y x^{2}$

Step 8.1.2.2

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

$6 y^{2 + 1} - 4 y (x^{2} y) + 3 y x^{2}$

Step 8.1.3

Add $2$ and $1$ .

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

Step 8.2

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

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Step 8.2.1

Move $y$ .

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

Step 8.2.2

Multiply $y$ by $y$ .

$6 y^{3} - 4 y^{2} x^{2} + 3 y x^{2}$