Algebra Examples

$(- 8 x^{8} - 40 x^{5}) \div (- 4 x^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{- 8 x^{8} - 40 x^{5}}{- 4 x^{2}}$

Step 2

Factor $8 x^{5}$ out of $- 8 x^{8} - 40 x^{5}$ .

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Step 2.1

Factor $8 x^{5}$ out of $- 8 x^{8}$ .

$\frac{8 x^{5} (- x^{3}) - 40 x^{5}}{- 4 x^{2}}$

Step 2.2

Factor $8 x^{5}$ out of $- 40 x^{5}$ .

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

Step 2.3

Factor $8 x^{5}$ out of $8 x^{5} (- x^{3}) + 8 x^{5} (- 5)$ .

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

Step 3

Cancel the common factor of $8$ and $- 4$ .

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Step 3.1

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

$\frac{4 (2 x^{5} (- x^{3} - 5))}{- 4 x^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $- 4 x^{2}$ .

$\frac{4 (2 x^{5} (- x^{3} - 5))}{4 (- x^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{4 (2 x^{5} (- x^{3} - 5))}{4 (- x^{2})}$

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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Step 4.1

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

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

Step 4.2

Move the negative one from the denominator of $\frac{2 x^{3} (- x^{3} - 5)}{- 1}$ .

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

Step 5

Rewrite $- 1 \cdot (2 x^{3} (- x^{3} - 5))$ as $- (2 x^{3} (- x^{3} - 5))$ .

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

Step 6

Apply the distributive property.

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

Step 7

Rewrite using the commutative property of multiplication.

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

Step 8

Multiply $- 5$ by $2$ .

$- (2 \cdot - 1 x^{3} x^{3} - 10 x^{3})$

Step 9

Simplify each term.

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Step 9.1

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

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Step 9.1.1

Move $x^{3}$ .

$- (2 \cdot - 1 (x^{3} x^{3}) - 10 x^{3})$

Step 9.1.2

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

$- (2 \cdot - 1 x^{3 + 3} - 10 x^{3})$

Step 9.1.3

Add $3$ and $3$ .

$- (2 \cdot - 1 x^{6} - 10 x^{3})$

Step 9.2

Multiply $2$ by $- 1$ .

$- (- 2 x^{6} - 10 x^{3})$

Step 10

Apply the distributive property.

$- (- 2 x^{6}) - (- 10 x^{3})$

Step 11

Multiply $- 2$ by $- 1$ .

$2 x^{6} - (- 10 x^{3})$

Step 12

Multiply $- 10$ by $- 1$ .

$2 x^{6} + 10 x^{3}$