Basic Math Examples

$\frac{3 a - 4 a^{3} - a}{- a}$

Step 1

Simplify the numerator.

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Step 1.1

Subtract $a$ from $3 a$ .

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

Step 1.2

Factor $2 a$ out of $- 4 a^{3} + 2 a$ .

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Step 1.2.1

Factor $2 a$ out of $- 4 a^{3}$ .

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

Step 1.2.2

Factor $2 a$ out of $2 a$ .

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

Step 1.2.3

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

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $a$ .

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Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Rewrite the expression.

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

Step 2.1.3

Move the negative one from the denominator of $\frac{2 (- 2 a^{2} + 1)}{- 1}$ .

$- 1 \cdot (2 (- 2 a^{2} + 1))$

Step 2.2

Rewrite $- 1 \cdot (2 (- 2 a^{2} + 1))$ as $- (2 (- 2 a^{2} + 1))$ .

$- (2 (- 2 a^{2} + 1))$

Step 2.3

Apply the distributive property.

$- (2 (- 2 a^{2}) + 2 \cdot 1)$

Step 2.4

Multiply.

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Step 2.4.1

Multiply $- 2$ by $2$ .

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

Step 2.4.2

Multiply $2$ by $1$ .

$- (- 4 a^{2} + 2)$

Step 2.5

Apply the distributive property.

$- (- 4 a^{2}) - 1 \cdot 2$

Step 2.6

Multiply.

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Step 2.6.1

Multiply $- 4$ by $- 1$ .

$4 a^{2} - 1 \cdot 2$

Step 2.6.2

Multiply $- 1$ by $2$ .

$4 a^{2} - 2$