Algebra Examples

$\frac{64 x^{4} - 88 x^{8}}{- 8 x^{3}}$

Step 1

Factor $8 x^{4}$ out of $64 x^{4} - 88 x^{8}$ .

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Step 1.1

Factor $8 x^{4}$ out of $64 x^{4}$ .

$\frac{8 x^{4} (8) - 88 x^{8}}{- 8 x^{3}}$

Step 1.2

Factor $8 x^{4}$ out of $- 88 x^{8}$ .

$\frac{8 x^{4} (8) + 8 x^{4} (- 11 x^{4})}{- 8 x^{3}}$

Step 1.3

Factor $8 x^{4}$ out of $8 x^{4} (8) + 8 x^{4} (- 11 x^{4})$ .

$\frac{8 x^{4} (8 - 11 x^{4})}{- 8 x^{3}}$

Step 2

Cancel the common factor of $8$ and $- 8$ .

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Step 2.1

Factor $8$ out of $8 x^{4} (8 - 11 x^{4})$ .

$\frac{8 (x^{4} (8 - 11 x^{4}))}{- 8 x^{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $8$ out of $- 8 x^{3}$ .

$\frac{8 (x^{4} (8 - 11 x^{4}))}{8 (- x^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{8 (x^{4} (8 - 11 x^{4}))}{8 (- x^{3})}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{4} (8 - 11 x^{4})}{- x^{3}}$

Step 3

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

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Step 3.1

Factor $x^{3}$ out of $x^{4} (8 - 11 x^{4})$ .

$\frac{x^{3} (x (8 - 11 x^{4}))}{- x^{3}}$

Step 3.2

Move the negative one from the denominator of $\frac{x (8 - 11 x^{4})}{- 1}$ .

$- 1 \cdot (x (8 - 11 x^{4}))$

Step 4

Rewrite $- 1 \cdot (x (8 - 11 x^{4}))$ as $- (x (8 - 11 x^{4}))$ .

$- (x (8 - 11 x^{4}))$

Step 5

Apply the distributive property.

$- (x \cdot 8 + x (- 11 x^{4}))$

Step 6

Move $8$ to the left of $x$ .

$- (8 \cdot x + x (- 11 x^{4}))$

Step 7

Rewrite using the commutative property of multiplication.

$- (8 \cdot x - 11 x \cdot x^{4})$

Step 8

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

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Step 8.1

Move $x^{4}$ .

$- (8 x - 11 (x^{4} x))$

Step 8.2

Multiply $x^{4}$ by $x$ .

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Step 8.2.1

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

$- (8 x - 11 (x^{4} x^{1}))$

Step 8.2.2

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

$- (8 x - 11 x^{4 + 1})$

Step 8.3

Add $4$ and $1$ .

$- (8 x - 11 x^{5})$

Step 9

Apply the distributive property.

$- (8 x) - (- 11 x^{5})$

Step 10

Multiply $8$ by $- 1$ .

$- 8 x - (- 11 x^{5})$

Step 11

Multiply $- 11$ by $- 1$ .

$- 8 x + 11 x^{5}$