Simplify 1/6(30x-24y)-1/8(32x-16y)

$\frac{1}{6} (30 x - 24 y) - \frac{1}{8} (32 x - 16 y)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{1}{6} (30 x) + \frac{1}{6} (- 24 y) - \frac{1}{8} \cdot (32 x - 16 y)$

Cancel the common factor of $6$ .

Factor $6$ out of $30 x$ .

$\frac{1}{6} (6 (5 x)) + \frac{1}{6} (- 24 y) - \frac{1}{8} \cdot (32 x - 16 y)$

Cancel the common factor.

$\frac{1}{6} (6 (5 x)) + \frac{1}{6} (- 24 y) - \frac{1}{8} \cdot (32 x - 16 y)$

Rewrite the expression.

$5 x + \frac{1}{6} (- 24 y) - \frac{1}{8} \cdot (32 x - 16 y)$

Cancel the common factor of $6$ .

Factor $6$ out of $- 24 y$ .

$5 x + \frac{1}{6} (6 (- 4 y)) - \frac{1}{8} \cdot (32 x - 16 y)$

Cancel the common factor.

$5 x + \frac{1}{6} (6 (- 4 y)) - \frac{1}{8} \cdot (32 x - 16 y)$

Rewrite the expression.

$5 x - 4 y - \frac{1}{8} \cdot (32 x - 16 y)$

Apply the distributive property.

$5 x - 4 y - \frac{1}{8} (32 x) - \frac{1}{8} (- 16 y)$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$5 x - 4 y + \frac{- 1}{8} (32 x) - \frac{1}{8} (- 16 y)$

Factor $8$ out of $32 x$ .

$5 x - 4 y + \frac{- 1}{8} (8 (4 x)) - \frac{1}{8} (- 16 y)$

Cancel the common factor.

$5 x - 4 y + \frac{- 1}{8} (8 (4 x)) - \frac{1}{8} (- 16 y)$

Rewrite the expression.

$5 x - 4 y - 1 (4 x) - \frac{1}{8} (- 16 y)$

Multiply $4$ by $- 1$ .

$5 x - 4 y - 4 x - \frac{1}{8} (- 16 y)$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$5 x - 4 y - 4 x + \frac{- 1}{8} (- 16 y)$

Factor $8$ out of $- 16 y$ .

$5 x - 4 y - 4 x + \frac{- 1}{8} (8 (- 2 y))$

Cancel the common factor.

$5 x - 4 y - 4 x + \frac{- 1}{8} (8 (- 2 y))$

Rewrite the expression.

$5 x - 4 y - 4 x - 1 (- 2 y)$

Multiply $- 2$ by $- 1$ .

$5 x - 4 y - 4 x + 2 y$

Step 2

Simplify by adding terms.

Subtract $4 x$ from $5 x$ .

$x - 4 y + 2 y$

Add $- 4 y$ and $2 y$ .

$x - 2 y$

Simplify 1/6(30x-24y)-1/8(32x-16y)

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