Expand the Trigonometric Expression 1/3(2/5-2/3w)

$\frac{1}{3} (\frac{2}{5} - \frac{2}{3} w)$

Step 1

Simplify each term.

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

$\frac{1}{3} (\frac{2}{5} - \frac{w \cdot 2}{3})$

Move $2$ to the left of $w$ .

$\frac{1}{3} (\frac{2}{5} - \frac{2 w}{3})$

Step 2

Apply the distributive property.

$\frac{1}{3} \cdot \frac{2}{5} + \frac{1}{3} (- \frac{2 w}{3})$

Step 3

Multiply $\frac{1}{3} \cdot \frac{2}{5}$ .

Multiply $\frac{1}{3}$ by $\frac{2}{5}$ .

$\frac{2}{3 \cdot 5} + \frac{1}{3} (- \frac{2 w}{3})$

Multiply $3$ by $5$ .

$\frac{2}{15} + \frac{1}{3} (- \frac{2 w}{3})$

Step 4

Multiply $\frac{1}{3} (- \frac{2 w}{3})$ .

Multiply $\frac{1}{3}$ by $\frac{2 w}{3}$ .

$\frac{2}{15} - \frac{2 w}{3 \cdot 3}$

Multiply $3$ by $3$ .

$\frac{2}{15} - \frac{2 w}{9}$