Basic Math Examples

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

Step 1

Factor $3$ out of $3 a + 6 \cdot (- 2^{3} a - \frac{3}{2} a)$ .

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Step 1.1

Factor $3$ out of $3 a$ .

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

Step 1.2

Factor $3$ out of $6 \cdot (- 2^{3} a - \frac{3}{2} a)$ .

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

Step 1.3

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

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

Step 2

Simplify each term.

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Step 2.1

Raise $2$ to the power of $3$ .

$3 (a + 2 \cdot (- 1 \cdot 8 a - \frac{3}{2} a))$

Step 2.2

Multiply $- 1$ by $8$ .

$3 (a + 2 \cdot (- 8 a - \frac{3}{2} a))$

Step 2.3

Combine $a$ and $\frac{3}{2}$ .

$3 (a + 2 \cdot (- 8 a - \frac{a \cdot 3}{2}))$

Step 2.4

Move $3$ to the left of $a$ .

$3 (a + 2 \cdot (- 8 a - \frac{3 \cdot a}{2}))$

Step 2.5

Multiply $3$ by $a$ .

$3 (a + 2 \cdot (- 8 a - \frac{3 a}{2}))$

Step 3

To write $- 8 a$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 (a + 2 \cdot (- 8 a \cdot \frac{2}{2} - \frac{3 a}{2}))$

Step 4

Combine $- 8 a$ and $\frac{2}{2}$ .

$3 (a + 2 \cdot (\frac{- 8 a \cdot 2}{2} - \frac{3 a}{2}))$

Step 5

Combine the numerators over the common denominator.

$3 (a + 2 \cdot \frac{- 8 a \cdot 2 - 3 a}{2})$

Step 6

Simplify the numerator.

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Step 6.1

Factor $a$ out of $- 8 a \cdot 2 - 3 a$ .

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Step 6.1.1

Factor $a$ out of $- 8 a \cdot 2$ .

$3 (a + 2 \cdot \frac{a (- 8 \cdot 2) - 3 a}{2})$

Step 6.1.2

Factor $a$ out of $- 3 a$ .

$3 (a + 2 \cdot \frac{a (- 8 \cdot 2) + a \cdot - 3}{2})$

Step 6.1.3

Factor $a$ out of $a (- 8 \cdot 2) + a \cdot - 3$ .

$3 (a + 2 \cdot \frac{a (- 8 \cdot 2 - 3)}{2})$

Step 6.2

Multiply $- 8$ by $2$ .

$3 (a + 2 \cdot \frac{a (- 16 - 3)}{2})$

Step 6.3

Subtract $3$ from $- 16$ .

$3 (a + 2 \cdot \frac{a \cdot - 19}{2})$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Cancel the common factor.

$3 (a + 2 \cdot \frac{a \cdot - 19}{2})$

Step 7.2

Rewrite the expression.

$3 (a + a \cdot - 19)$

Step 8

Move $- 19$ to the left of $a$ .

$3 (a - 19 a)$

Step 9

Factor.

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Step 9.1

Subtract $19 a$ from $a$ .

$3 (- 18 a)$

Step 9.2

Remove unnecessary parentheses.

$3 \cdot - 18 a$

Step 10

Multiply $3$ by $- 18$ .

$- 54 a$