Pre-Algebra Examples

$\frac{- 10 x^{10} + 20 x^{6}}{- 5 x^{2}}$

Step 1

Factor $10 x^{6}$ out of $- 10 x^{10} + 20 x^{6}$ .

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Step 1.1

Factor $10 x^{6}$ out of $- 10 x^{10}$ .

$\frac{10 x^{6} (- x^{4}) + 20 x^{6}}{- 5 x^{2}}$

Step 1.2

Factor $10 x^{6}$ out of $20 x^{6}$ .

$\frac{10 x^{6} (- x^{4}) + 10 x^{6} (2)}{- 5 x^{2}}$

Step 1.3

Factor $10 x^{6}$ out of $10 x^{6} (- x^{4}) + 10 x^{6} (2)$ .

$\frac{10 x^{6} (- x^{4} + 2)}{- 5 x^{2}}$

Step 2

Cancel the common factor of $10$ and $- 5$ .

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Step 2.1

Factor $5$ out of $10 x^{6} (- x^{4} + 2)$ .

$\frac{5 (2 x^{6} (- x^{4} + 2))}{- 5 x^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $- 5 x^{2}$ .

$\frac{5 (2 x^{6} (- x^{4} + 2))}{5 (- x^{2})}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (2 x^{6} (- x^{4} + 2))}{5 (- x^{2})}$

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{6}$ and $x^{2}$ .

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Step 3.1

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

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

Step 3.2

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

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

Step 4

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

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

Step 5

Apply the distributive property.

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

Step 6

Rewrite using the commutative property of multiplication.

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

Step 7

Multiply $2$ by $2$ .

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

Step 8

Simplify each term.

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Step 8.1

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

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Step 8.1.1

Move $x^{4}$ .

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

Step 8.1.2

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

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

Step 8.1.3

Add $4$ and $4$ .

$- (2 \cdot - 1 x^{8} + 4 x^{4})$

Step 8.2

Multiply $2$ by $- 1$ .

$- (- 2 x^{8} + 4 x^{4})$

Step 9

Apply the distributive property.

$- (- 2 x^{8}) - (4 x^{4})$

Step 10

Multiply $- 2$ by $- 1$ .

$2 x^{8} - (4 x^{4})$

Step 11

Multiply $4$ by $- 1$ .

$2 x^{8} - 4 x^{4}$