Pre-Algebra Examples

$\frac{12 x^{8} - 18 x^{7} + 30 x^{2}}{6 x}$

Step 1

Factor $6 x^{2}$ out of $12 x^{8} - 18 x^{7} + 30 x^{2}$ .

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Step 1.1

Factor $6 x^{2}$ out of $12 x^{8}$ .

$\frac{6 x^{2} (2 x^{6}) - 18 x^{7} + 30 x^{2}}{6 x}$

Step 1.2

Factor $6 x^{2}$ out of $- 18 x^{7}$ .

$\frac{6 x^{2} (2 x^{6}) + 6 x^{2} (- 3 x^{5}) + 30 x^{2}}{6 x}$

Step 1.3

Factor $6 x^{2}$ out of $30 x^{2}$ .

$\frac{6 x^{2} (2 x^{6}) + 6 x^{2} (- 3 x^{5}) + 6 x^{2} (5)}{6 x}$

Step 1.4

Factor $6 x^{2}$ out of $6 x^{2} (2 x^{6}) + 6 x^{2} (- 3 x^{5})$ .

$\frac{6 x^{2} (2 x^{6} - 3 x^{5}) + 6 x^{2} (5)}{6 x}$

Step 1.5

Factor $6 x^{2}$ out of $6 x^{2} (2 x^{6} - 3 x^{5}) + 6 x^{2} (5)$ .

$\frac{6 x^{2} (2 x^{6} - 3 x^{5} + 5)}{6 x}$

Step 2

Cancel the common factor of $6$ .

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Step 2.1

Cancel the common factor.

$\frac{6 x^{2} (2 x^{6} - 3 x^{5} + 5)}{6 x}$

Step 2.2

Rewrite the expression.

$\frac{x^{2} (2 x^{6} - 3 x^{5} + 5)}{x}$

Step 3

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

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Step 3.1

Factor $x$ out of $x^{2} (2 x^{6} - 3 x^{5} + 5)$ .

$\frac{x (x (2 x^{6} - 3 x^{5} + 5))}{x}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{x (x (2 x^{6} - 3 x^{5} + 5))}{x^{1}}$

Step 3.2.2

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

$\frac{x (x (2 x^{6} - 3 x^{5} + 5))}{x \cdot 1}$

Step 3.2.3

Cancel the common factor.

$\frac{x (x (2 x^{6} - 3 x^{5} + 5))}{x \cdot 1}$

Step 3.2.4

Rewrite the expression.

$\frac{x (2 x^{6} - 3 x^{5} + 5)}{1}$

Step 3.2.5

Divide $x (2 x^{6} - 3 x^{5} + 5)$ by $1$ .

$x (2 x^{6} - 3 x^{5} + 5)$

Step 4

Apply the distributive property.

$x (2 x^{6}) + x (- 3 x^{5}) + x \cdot 5$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$2 x \cdot x^{6} + x (- 3 x^{5}) + x \cdot 5$

Step 5.2

Rewrite using the commutative property of multiplication.

$2 x \cdot x^{6} - 3 x \cdot x^{5} + x \cdot 5$

Step 5.3

Move $5$ to the left of $x$ .

$2 x \cdot x^{6} - 3 x \cdot x^{5} + 5 \cdot x$

Step 6

Simplify each term.

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Step 6.1

Multiply $x$ by $x^{6}$ by adding the exponents.

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Step 6.1.1

Move $x^{6}$ .

$2 (x^{6} x) - 3 x \cdot x^{5} + 5 \cdot x$

Step 6.1.2

Multiply $x^{6}$ by $x$ .

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Step 6.1.2.1

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

$2 (x^{6} x^{1}) - 3 x \cdot x^{5} + 5 \cdot x$

Step 6.1.2.2

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

$2 x^{6 + 1} - 3 x \cdot x^{5} + 5 \cdot x$

Step 6.1.3

Add $6$ and $1$ .

$2 x^{7} - 3 x \cdot x^{5} + 5 \cdot x$

Step 6.2

Multiply $x$ by $x^{5}$ by adding the exponents.

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Step 6.2.1

Move $x^{5}$ .

$2 x^{7} - 3 (x^{5} x) + 5 \cdot x$

Step 6.2.2

Multiply $x^{5}$ by $x$ .

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Step 6.2.2.1

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

$2 x^{7} - 3 (x^{5} x^{1}) + 5 \cdot x$

Step 6.2.2.2

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

$2 x^{7} - 3 x^{5 + 1} + 5 \cdot x$

Step 6.2.3

Add $5$ and $1$ .

$2 x^{7} - 3 x^{6} + 5 \cdot x$

$2 x^{7} - 3 x^{6} + 5 x$