Pre-Algebra Examples

$(21 a^{5} - 35 a^{4} - 35 a^{3} \cdot (21 a)) \div (- 7 a)$

Step 1

Factor $7 a^{3}$ out of $21 a^{5} - 35 a^{4} - 35 a^{3} \cdot (21 a)$ .

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Step 1.1

Factor $7 a^{3}$ out of $21 a^{5}$ .

$(7 a^{3} (3 a^{2}) - 35 a^{4} - 35 a^{3} \cdot (21 a)) \div (- 7 a)$

Step 1.2

Factor $7 a^{3}$ out of $- 35 a^{4}$ .

$(7 a^{3} (3 a^{2}) + 7 a^{3} (- 5 a) - 35 a^{3} \cdot (21 a)) \div (- 7 a)$

Step 1.3

Factor $7 a^{3}$ out of $- 35 a^{3} \cdot (21 a)$ .

$(7 a^{3} (3 a^{2}) + 7 a^{3} (- 5 a) + 7 a^{3} (- 5 \cdot (21 a))) \div (- 7 a)$

Step 1.4

Factor $7 a^{3}$ out of $7 a^{3} (3 a^{2}) + 7 a^{3} (- 5 a)$ .

$(7 a^{3} (3 a^{2} - 5 a) + 7 a^{3} (- 5 \cdot (21 a))) \div (- 7 a)$

Step 1.5

Factor $7 a^{3}$ out of $7 a^{3} (3 a^{2} - 5 a) + 7 a^{3} (- 5 \cdot (21 a))$ .

$7 a^{3} (3 a^{2} - 5 a - 5 \cdot (21 a)) \div (- 7 a)$

Step 2

Multiply $21$ by $- 5$ .

$7 a^{3} (3 a^{2} - 5 a - 105 \cdot a) \div (- 7 a)$

Step 3

Reduce the expression $7 a^{3} (3 a^{2} - 5 a - 105 \cdot a) \div (- 7 a)$ by cancelling the common factors.

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Step 3.1

Factor $7$ out of $7 a^{3} (3 a^{2} - 5 a - 105 \cdot a)$ .

$7 (a^{3} (3 a^{2} - 5 a - 105 \cdot a)) \div (- 7 a)$

Step 3.2

Factor $7$ out of $- 7 a$ .

$7 (a^{3} (3 a^{2} - 5 a - 105 \cdot a)) \div 7 (- a)$

Step 3.3

Cancel the common factor.

$7 (a^{3} (3 a^{2} - 5 a - 105 \cdot a)) \div 7 (- a)$

Step 3.4

Rewrite the expression.

$\frac{a^{3} (3 a^{2} - 5 a - 105 \cdot a)}{- a}$

Step 4

Subtract $105 \cdot a$ from $- 5 a$ .

$\frac{a^{3} (3 a^{2} - 110 a)}{- a}$

Step 5

Factor.

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Step 5.1

Factor $a$ out of $3 a^{2} - 110 a$ .

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Step 5.1.1

Factor $a$ out of $3 a^{2}$ .

$\frac{a^{3} (a (3 a) - 110 a)}{- a}$

Step 5.1.2

Factor $a$ out of $- 110 a$ .

$\frac{a^{3} (a (3 a) + a \cdot - 110)}{- a}$

Step 5.1.3

Factor $a$ out of $a (3 a) + a \cdot - 110$ .

$\frac{a^{3} (a (3 a - 110))}{- a}$

Step 5.2

Remove unnecessary parentheses.

$\frac{a^{3} a (3 a - 110)}{- a}$

Step 6

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

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Step 6.1

Multiply $a^{3}$ by $a$ .

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Step 6.1.1

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

$\frac{a^{3} a^{1} (3 a - 110)}{- a}$

Step 6.1.2

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

$\frac{a^{3 + 1} (3 a - 110)}{- a}$

Step 6.2

Add $3$ and $1$ .

$\frac{a^{4} (3 a - 110)}{- a}$

Step 7

Reduce the expression $\frac{a^{4} (3 a - 110)}{- a}$ by cancelling the common factors.

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Step 7.1

Factor $a$ out of $a^{4} (3 a - 110)$ .

$\frac{a (a^{3} (3 a - 110))}{- a}$

Step 7.2

Factor $a$ out of $- a$ .

$\frac{a (a^{3} (3 a - 110))}{a \cdot - 1}$

Step 7.3

Cancel the common factor.

$\frac{a (a^{3} (3 a - 110))}{a \cdot - 1}$

Step 7.4

Rewrite the expression.

$\frac{a^{3} (3 a - 110)}{- 1}$

Step 8

Move the negative one from the denominator of $\frac{a^{3} (3 a - 110)}{- 1}$ .

$- 1 \cdot (a^{3} (3 a - 110))$