Pre-Algebra Examples

$\frac{8 x^{5} + 4 x^{3}}{- x^{2}}$

Step 1

Simplify terms.

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Step 1.1

Factor $4 x^{3}$ out of $8 x^{5} + 4 x^{3}$ .

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Step 1.1.1

Factor $4 x^{3}$ out of $8 x^{5}$ .

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

Step 1.1.2

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

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

Step 1.1.3

Factor $4 x^{3}$ out of $4 x^{3} (2 x^{2}) + 4 x^{3} (1)$ .

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

Step 1.2

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 1.2.1

Factor $x^{2}$ out of $4 x^{3} (2 x^{2} + 1)$ .

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

Step 1.2.2

Move the negative one from the denominator of $\frac{4 x (2 x^{2} + 1)}{- 1}$ .

$- 1 \cdot (4 x (2 x^{2} + 1))$

Step 1.3

Rewrite $- 1 \cdot (4 x (2 x^{2} + 1))$ as $- (4 x (2 x^{2} + 1))$ .

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

Step 1.4

Apply the distributive property.

$- (4 x (2 x^{2}) + 4 x \cdot 1)$

Step 1.5

Simplify the expression.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$- (4 \cdot 2 x \cdot x^{2} + 4 x \cdot 1)$

Step 1.5.2

Multiply $4$ by $1$ .

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

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $x^{2}$ .

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

Step 2.1.2

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

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Step 2.1.2.1

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

$- (4 \cdot 2 (x^{2} x^{1}) + 4 x)$

Step 2.1.2.2

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

$- (4 \cdot 2 x^{2 + 1} + 4 x)$

Step 2.1.3

Add $2$ and $1$ .

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

Step 2.2

Multiply $4$ by $2$ .

$- (8 x^{3} + 4 x)$

Step 3

Simplify by multiplying through.

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Step 3.1

Apply the distributive property.

$- (8 x^{3}) - (4 x)$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $8$ by $- 1$ .

$- 8 x^{3} - (4 x)$

Step 3.2.2

Multiply $4$ by $- 1$ .

$- 8 x^{3} - 4 x$