Pre-Algebra Examples

$- 4 a^{2} + 6 a^{3 - 10 - 4 a \div 3 a - 5}$

Step 1

The polynomial cannot be factored using the grouping method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the grouping method.

Step 2

Factor $2$ out of $- 4 a^{2} + 6 a^{3 - 10 - 4 a \div 3 a - 5}$ .

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Step 2.1

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

$2 (- 2 a^{2}) + 6 a^{3 - 10 - 4 a \div 3 a - 5}$

Step 2.2

Factor $2$ out of $6 a^{3 - 10 - 4 a \div 3 a - 5}$ .

$2 (- 2 a^{2}) + 2 (3 a^{3 - 10 - 4 a \div 3 a - 5})$

Step 2.3

Factor $2$ out of $2 (- 2 a^{2}) + 2 (3 a^{3 - 10 - 4 a \div 3 a - 5})$ .

$2 (- 2 a^{2} + 3 a^{3 - 10 - 4 a \div 3 a - 5})$

Step 3

Simplify each term.

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Step 3.1

Rewrite the division as a fraction.

$2 (- 2 a^{2} + 3 a^{3 - 10 - \frac{4 a}{3} a - 5})$

Step 3.2

Multiply $- \frac{4 a}{3} a$ .

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Step 3.2.1

Combine $a$ and $\frac{4 a}{3}$ .

$2 (- 2 a^{2} + 3 a^{3 - 10 - \frac{a (4 a)}{3} - 5})$

Step 3.2.2

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

$2 (- 2 a^{2} + 3 a^{3 - 10 - \frac{4 (a^{1} a)}{3} - 5})$

Step 3.2.3

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

$2 (- 2 a^{2} + 3 a^{3 - 10 - \frac{4 (a^{1} a^{1})}{3} - 5})$

Step 3.2.4

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

$2 (- 2 a^{2} + 3 a^{3 - 10 - \frac{4 a^{1 + 1}}{3} - 5})$

Step 3.2.5

Add $1$ and $1$ .

$2 (- 2 a^{2} + 3 a^{3 - 10 - \frac{4 a^{2}}{3} - 5})$

Step 4

Subtract $10$ from $3$ .

$2 (- 2 a^{2} + 3 a^{- 7 - \frac{4 a^{2}}{3} - 5})$

Step 5

Subtract $5$ from $- 7$ .

$2 (- 2 a^{2} + 3 a^{- \frac{4 a^{2}}{3} - 12})$