Basic Math Examples

$\frac{2}{3} \cdot (- 18 a + 21 b) + (\frac{- 1}{3}) (15 a + 12 b)$

Step 1

Factor $\frac{1}{3}$ out of each term.

$\frac{1}{3} \cdot (2 (- 18 a + 21 b) - (15 a + 12 b))$

Step 2

Apply the distributive property.

$\frac{1}{3} \cdot (2 (- 18 a) + 2 (21 b) - (15 a + 12 b))$

Step 3

Multiply $- 18$ by $2$ .

$\frac{1}{3} \cdot (- 36 a + 2 (21 b) - (15 a + 12 b))$

Step 4

Multiply $21$ by $2$ .

$\frac{1}{3} \cdot (- 36 a + 42 b - (15 a + 12 b))$

Step 5

Apply the distributive property.

$\frac{1}{3} \cdot (- 36 a + 42 b - (15 a) - (12 b))$

Step 6

Multiply $15$ by $- 1$ .

$\frac{1}{3} \cdot (- 36 a + 42 b - 15 a - (12 b))$

Step 7

Multiply $12$ by $- 1$ .

$\frac{1}{3} \cdot (- 36 a + 42 b - 15 a - 12 b)$

Step 8

Subtract $15 a$ from $- 36 a$ .

$\frac{1}{3} \cdot (- 51 a + 42 b - 12 b)$

Step 9

Subtract $12 b$ from $42 b$ .

$\frac{1}{3} \cdot (- 51 a + 30 b)$

Step 10

Factor.

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Step 10.1

Factor $- 3$ out of $- 51 a + 30 b$ .

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Step 10.1.1

Factor $- 3$ out of $- 51 a$ .

$\frac{1}{3} \cdot (- 3 (17 a) + 30 b)$

Step 10.1.2

Factor $- 3$ out of $30 b$ .

$\frac{1}{3} \cdot (- 3 (17 a) - 3 (- 10 b))$

Step 10.1.3

Factor $- 3$ out of $- 3 (17 a) - 3 (- 10 b)$ .

$\frac{1}{3} \cdot (- 3 (17 a - 10 b))$

Step 10.2

Remove unnecessary parentheses.

$\frac{1}{3} \cdot - 3 (17 a - 10 b)$

Step 11

Combine $\frac{1}{3}$ and $- 3$ .

$\frac{- 3}{3} (17 a - 10 b)$

Step 12

Divide $- 3$ by $3$ .

$- 1 \cdot (17 a - 10 b)$