Simplify 2/3y-2(4/3y+z)

$\frac{2}{3} y - 2 (\frac{4}{3} y + z)$

Step 1

Simplify each term.

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

$\frac{2 y}{3} - 2 (\frac{4}{3} y + z)$

Combine $\frac{4}{3}$ and $y$ .

$\frac{2 y}{3} - 2 (\frac{4 y}{3} + z)$

Apply the distributive property.

$\frac{2 y}{3} - 2 \frac{4 y}{3} - 2 z$

Multiply $- 2 \frac{4 y}{3}$ .

Combine $- 2$ and $\frac{4 y}{3}$ .

$\frac{2 y}{3} + \frac{- 2 (4 y)}{3} - 2 z$

Multiply $4$ by $- 2$ .

$\frac{2 y}{3} + \frac{- 8 y}{3} - 2 z$

$\frac{2 y}{3} + \frac{- 8 y}{3} - 2 z$

Move the negative in front of the fraction.

$\frac{2 y}{3} - \frac{8 y}{3} - 2 z$

$\frac{2 y}{3} - \frac{8 y}{3} - 2 z$

Step 2

Simplify terms.

Combine the numerators over the common denominator.

$- 2 z + \frac{2 y - 8 y}{3}$

Subtract $8 y$ from $2 y$ .

$- 2 z + \frac{- 6 y}{3}$

Cancel the common factor of $- 6$ and $3$ .

Factor $3$ out of $- 6 y$ .

$- 2 z + \frac{3 (- 2 y)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$- 2 z + \frac{3 (- 2 y)}{3 (1)}$

Cancel the common factor.

$- 2 z + \frac{3 (- 2 y)}{3 \cdot 1}$

Rewrite the expression.

$- 2 z + \frac{- 2 y}{1}$

Divide $- 2 y$ by $1$ .

$- 2 z - 2 y$

$- 2 z - 2 y$

$- 2 z - 2 y$

$- 2 z - 2 y$

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