Pre-Algebra Examples

$\frac{28 x^{6} - 24 x^{4}}{4 x^{3}}$

Step 1

Factor $4 x^{4}$ out of $28 x^{6} - 24 x^{4}$ .

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Step 1.1

Factor $4 x^{4}$ out of $28 x^{6}$ .

$\frac{4 x^{4} (7 x^{2}) - 24 x^{4}}{4 x^{3}}$

Step 1.2

Factor $4 x^{4}$ out of $- 24 x^{4}$ .

$\frac{4 x^{4} (7 x^{2}) + 4 x^{4} (- 6)}{4 x^{3}}$

Step 1.3

Factor $4 x^{4}$ out of $4 x^{4} (7 x^{2}) + 4 x^{4} (- 6)$ .

$\frac{4 x^{4} (7 x^{2} - 6)}{4 x^{3}}$

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Cancel the common factor.

$\frac{4 x^{4} (7 x^{2} - 6)}{4 x^{3}}$

Step 2.2

Rewrite the expression.

$\frac{x^{4} (7 x^{2} - 6)}{x^{3}}$

Step 3

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

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Step 3.1

Factor $x^{3}$ out of $x^{4} (7 x^{2} - 6)$ .

$\frac{x^{3} (x (7 x^{2} - 6))}{x^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{x^{3} (x (7 x^{2} - 6))}{x^{3} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{3} (x (7 x^{2} - 6))}{x^{3} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{x (7 x^{2} - 6)}{1}$

Step 3.2.4

Divide $x (7 x^{2} - 6)$ by $1$ .

$x (7 x^{2} - 6)$

Step 4

Apply the distributive property.

$x (7 x^{2}) + x \cdot - 6$

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

Move $- 6$ to the left of $x$ .

$7 x \cdot x^{2} - 6 \cdot x$

Step 7

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

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Step 7.1

Move $x^{2}$ .

$7 (x^{2} x) - 6 \cdot x$

Step 7.2

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

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Step 7.2.1

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

$7 (x^{2} x^{1}) - 6 \cdot x$

Step 7.2.2

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

$7 x^{2 + 1} - 6 \cdot x$

Step 7.3

Add $2$ and $1$ .

$7 x^{3} - 6 \cdot x$

$7 x^{3} - 6 x$