Simplify 1/3(6ab-9b)+2/3(9ab+12b)

$\frac{1}{3} (6 a b - 9 b) + \frac{2}{3} (9 a b + 12 b)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{1}{3} (6 a b) + \frac{1}{3} (- 9 b) + \frac{2}{3} \cdot (9 a b + 12 b)$

Cancel the common factor of $3$ .

Factor $3$ out of $6 a b$ .

$\frac{1}{3} (3 (2 a b)) + \frac{1}{3} (- 9 b) + \frac{2}{3} \cdot (9 a b + 12 b)$

Cancel the common factor.

$\frac{1}{3} (3 (2 a b)) + \frac{1}{3} (- 9 b) + \frac{2}{3} \cdot (9 a b + 12 b)$

Rewrite the expression.

$2 a b + \frac{1}{3} (- 9 b) + \frac{2}{3} \cdot (9 a b + 12 b)$

Cancel the common factor of $3$ .

Factor $3$ out of $- 9 b$ .

$2 a b + \frac{1}{3} (3 (- 3 b)) + \frac{2}{3} \cdot (9 a b + 12 b)$

Cancel the common factor.

$2 a b + \frac{1}{3} (3 (- 3 b)) + \frac{2}{3} \cdot (9 a b + 12 b)$

Rewrite the expression.

$2 a b - 3 b + \frac{2}{3} \cdot (9 a b + 12 b)$

Apply the distributive property.

$2 a b - 3 b + \frac{2}{3} (9 a b) + \frac{2}{3} (12 b)$

Cancel the common factor of $3$ .

Factor $3$ out of $9 a b$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $2$ .

$2 a b - 3 b + 6 (a b) + \frac{2}{3} (12 b)$

Cancel the common factor of $3$ .

Factor $3$ out of $12 b$ .

$2 a b - 3 b + 6 (a b) + \frac{2}{3} (3 (4 b))$

Cancel the common factor.

$2 a b - 3 b + 6 (a b) + \frac{2}{3} (3 (4 b))$

Rewrite the expression.

$2 a b - 3 b + 6 (a b) + 2 (4 b)$

Multiply $4$ by $2$ .

$2 a b - 3 b + 6 a b + 8 b$

Step 2

Simplify by adding terms.

Add $2 a b$ and $6 a b$ .

$- 3 b + 8 a b + 8 b$

Add $- 3 b$ and $8 b$ .

$5 b + 8 a b$