Algebra Examples

$3 a^{3} - 5 a b^{2} - 6 a^{2} b^{3}$ entre $- 2 a$

Step 1

Write the problem as a mathematical expression.

$\frac{3 a^{3} - 5 a b^{2} - 6 a^{2} b^{3}}{- 2 a}$

Step 2

Factor $a$ out of $3 a^{3} - 5 a b^{2} - 6 a^{2} b^{3}$ .

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Step 2.1

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

$\frac{a (3 a^{2}) - 5 a b^{2} - 6 a^{2} b^{3}}{- 2 a}$

Step 2.2

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

$\frac{a (3 a^{2}) + a (- 5 b^{2}) - 6 a^{2} b^{3}}{- 2 a}$

Step 2.3

Factor $a$ out of $- 6 a^{2} b^{3}$ .

$\frac{a (3 a^{2}) + a (- 5 b^{2}) + a (- 6 a b^{3})}{- 2 a}$

Step 2.4

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

$\frac{a (3 a^{2} - 5 b^{2}) + a (- 6 a b^{3})}{- 2 a}$

Step 2.5

Factor $a$ out of $a (3 a^{2} - 5 b^{2}) + a (- 6 a b^{3})$ .

$\frac{a (3 a^{2} - 5 b^{2} - 6 a b^{3})}{- 2 a}$

Step 3

Cancel the common factor of $a$ .

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Step 3.1

Cancel the common factor.

$\frac{a (3 a^{2} - 5 b^{2} - 6 a b^{3})}{- 2 a}$

Step 3.2

Rewrite the expression.

$\frac{3 a^{2} - 5 b^{2} - 6 a b^{3}}{- 2}$

Step 4

Move the negative in front of the fraction.

$- \frac{3 a^{2} - 5 b^{2} - 6 a b^{3}}{2}$

Step 5

Split the fraction $\frac{3 a^{2} - 5 b^{2} - 6 a b^{3}}{2}$ into two fractions.

$- (\frac{3 a^{2} - 5 b^{2}}{2} + \frac{- 6 a b^{3}}{2})$

Step 6

Split the fraction $\frac{3 a^{2} - 5 b^{2}}{2}$ into two fractions.

$- (\frac{3 a^{2}}{2} + \frac{- 5 b^{2}}{2} + \frac{- 6 a b^{3}}{2})$

Step 7

Move the negative in front of the fraction.

$- (\frac{3 a^{2}}{2} - \frac{5 b^{2}}{2} + \frac{- 6 a b^{3}}{2})$

Step 8

Cancel the common factor of $- 6$ and $2$ .

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Step 8.1

Factor $2$ out of $- 6 a b^{3}$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $2$ .

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

Step 8.2.2

Cancel the common factor.

$- (\frac{3 a^{2}}{2} - \frac{5 b^{2}}{2} + \frac{2 (- 3 a b^{3})}{2 \cdot 1})$

Step 8.2.3

Rewrite the expression.

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

Step 8.2.4

Divide $- 3 a b^{3}$ by $1$ .

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