Pre-Algebra Examples

$(35 a^{4} - 42 a^{8} + 28 a^{2}) \div 7 a^{4}$

Step 1

Rewrite the division as a fraction.

$\frac{35 a^{4} - 42 a^{8} + 28 a^{2}}{7 a^{4}}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $7 a^{2}$ out of $35 a^{4} - 42 a^{8} + 28 a^{2}$ .

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Step 2.1.1

Factor $7 a^{2}$ out of $35 a^{4}$ .

$\frac{7 a^{2} (5 a^{2}) - 42 a^{8} + 28 a^{2}}{7 a^{4}}$

Step 2.1.2

Factor $7 a^{2}$ out of $- 42 a^{8}$ .

$\frac{7 a^{2} (5 a^{2}) + 7 a^{2} (- 6 a^{6}) + 28 a^{2}}{7 a^{4}}$

Step 2.1.3

Factor $7 a^{2}$ out of $28 a^{2}$ .

$\frac{7 a^{2} (5 a^{2}) + 7 a^{2} (- 6 a^{6}) + 7 a^{2} (4)}{7 a^{4}}$

Step 2.1.4

Factor $7 a^{2}$ out of $7 a^{2} (5 a^{2}) + 7 a^{2} (- 6 a^{6})$ .

$\frac{7 a^{2} (5 a^{2} - 6 a^{6}) + 7 a^{2} (4)}{7 a^{4}}$

Step 2.1.5

Factor $7 a^{2}$ out of $7 a^{2} (5 a^{2} - 6 a^{6}) + 7 a^{2} (4)$ .

$\frac{7 a^{2} (5 a^{2} - 6 a^{6} + 4)}{7 a^{4}}$

Step 2.2

Reorder terms.

$\frac{7 a^{2} (- 6 a^{6} + 5 a^{2} + 4)}{7 a^{4}}$

Step 3

Cancel the common factor of $7$ .

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Step 3.1

Cancel the common factor.

$\frac{7 a^{2} (- 6 a^{6} + 5 a^{2} + 4)}{7 a^{4}}$

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factors.

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Step 4.1

Factor $a^{2}$ out of $a^{4}$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$\frac{- 6 a^{6} + 5 a^{2} + 4}{a^{2}}$

Step 5

Factor $- 1$ out of $- 6 a^{6}$ .

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

Step 6

Factor $- 1$ out of $5 a^{2}$ .

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

Step 7

Factor $- 1$ out of $- (6 a^{6}) - (- 5 a^{2})$ .

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

Step 8

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{- (6 a^{6} - 5 a^{2}) - 1 (- 4)}{a^{2}}$

Step 9

Factor $- 1$ out of $- (6 a^{6} - 5 a^{2}) - 1 (- 4)$ .

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

Step 10

Rewrite $- (6 a^{6} - 5 a^{2} - 4)$ as $- 1 (6 a^{6} - 5 a^{2} - 4)$ .

$\frac{- 1 (6 a^{6} - 5 a^{2} - 4)}{a^{2}}$

Step 11

Move the negative in front of the fraction.

$- \frac{6 a^{6} - 5 a^{2} - 4}{a^{2}}$

Step 12

Split the fraction $\frac{6 a^{6} - 5 a^{2} - 4}{a^{2}}$ into two fractions.

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

Step 13

Split the fraction $\frac{6 a^{6} - 5 a^{2}}{a^{2}}$ into two fractions.

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

Step 14

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

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Step 14.1

Factor $a^{2}$ out of $6 a^{6}$ .

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

Step 14.2

Cancel the common factors.

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Step 14.2.1

Multiply by $1$ .

$- (\frac{a^{2} (6 a^{4})}{a^{2} \cdot 1} + \frac{- 5 a^{2}}{a^{2}} + \frac{- 4}{a^{2}})$

Step 14.2.2

Cancel the common factor.

$- (\frac{a^{2} (6 a^{4})}{a^{2} \cdot 1} + \frac{- 5 a^{2}}{a^{2}} + \frac{- 4}{a^{2}})$

Step 14.2.3

Rewrite the expression.

$- (\frac{6 a^{4}}{1} + \frac{- 5 a^{2}}{a^{2}} + \frac{- 4}{a^{2}})$

Step 14.2.4

Divide $6 a^{4}$ by $1$ .

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

Step 15

Cancel the common factor of $a^{2}$ .

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Step 15.1

Cancel the common factor.

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

Step 15.2

Divide $- 5$ by $1$ .

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

Step 16

Move the negative in front of the fraction.

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