Pre-Algebra Examples

$(63 x^{8} - 42 x^{6} - 35 x^{3}) \div (- 7 x^{3})$

Step 1

Rewrite the division as a fraction.

$\frac{63 x^{8} - 42 x^{6} - 35 x^{3}}{- 7 x^{3}}$

Step 2

Factor $7 x^{3}$ out of $63 x^{8} - 42 x^{6} - 35 x^{3}$ .

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Step 2.1

Factor $7 x^{3}$ out of $63 x^{8}$ .

$\frac{7 x^{3} (9 x^{5}) - 42 x^{6} - 35 x^{3}}{- 7 x^{3}}$

Step 2.2

Factor $7 x^{3}$ out of $- 42 x^{6}$ .

$\frac{7 x^{3} (9 x^{5}) + 7 x^{3} (- 6 x^{3}) - 35 x^{3}}{- 7 x^{3}}$

Step 2.3

Factor $7 x^{3}$ out of $- 35 x^{3}$ .

$\frac{7 x^{3} (9 x^{5}) + 7 x^{3} (- 6 x^{3}) + 7 x^{3} (- 5)}{- 7 x^{3}}$

Step 2.4

Factor $7 x^{3}$ out of $7 x^{3} (9 x^{5}) + 7 x^{3} (- 6 x^{3})$ .

$\frac{7 x^{3} (9 x^{5} - 6 x^{3}) + 7 x^{3} (- 5)}{- 7 x^{3}}$

Step 2.5

Factor $7 x^{3}$ out of $7 x^{3} (9 x^{5} - 6 x^{3}) + 7 x^{3} (- 5)$ .

$\frac{7 x^{3} (9 x^{5} - 6 x^{3} - 5)}{- 7 x^{3}}$

Step 3

Cancel the common factor of $7$ and $- 7$ .

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Step 3.1

Factor $7$ out of $7 x^{3} (9 x^{5} - 6 x^{3} - 5)$ .

$\frac{7 (x^{3} (9 x^{5} - 6 x^{3} - 5))}{- 7 x^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $7$ out of $- 7 x^{3}$ .

$\frac{7 (x^{3} (9 x^{5} - 6 x^{3} - 5))}{7 (- x^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{7 (x^{3} (9 x^{5} - 6 x^{3} - 5))}{7 (- x^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{3} (9 x^{5} - 6 x^{3} - 5)}{- x^{3}}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{x^{3} (9 x^{5} - 6 x^{3} - 5)}{- x^{3}}$

Step 4.2

Rewrite the expression.

$\frac{9 x^{5} - 6 x^{3} - 5}{- 1}$

Step 4.3

Move the negative one from the denominator of $\frac{9 x^{5} - 6 x^{3} - 5}{- 1}$ .

$- 1 \cdot (9 x^{5} - 6 x^{3} - 5)$

Step 5

Rewrite $- 1 \cdot (9 x^{5} - 6 x^{3} - 5)$ as $- (9 x^{5} - 6 x^{3} - 5)$ .

$- (9 x^{5} - 6 x^{3} - 5)$

Step 6

Apply the distributive property.

$- (9 x^{5}) - (- 6 x^{3}) - - 5$

Step 7

Simplify.

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Step 7.1

Multiply $9$ by $- 1$ .

$- 9 x^{5} - (- 6 x^{3}) - - 5$

Step 7.2

Multiply $- 6$ by $- 1$ .

$- 9 x^{5} + 6 x^{3} - - 5$

Step 7.3

Multiply $- 1$ by $- 5$ .

$- 9 x^{5} + 6 x^{3} + 5$