Simplify 1/8(-8c+16)-1/3(6+3c)

$\frac{1}{8} (- 8 c + 16) - \frac{1}{3} (6 + 3 c)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{1}{8} (- 8 c) + \frac{1}{8} \cdot 16 - \frac{1}{3} \cdot (6 + 3 c)$

Cancel the common factor of $8$ .

Factor $8$ out of $- 8 c$ .

$\frac{1}{8} (8 (- c)) + \frac{1}{8} \cdot 16 - \frac{1}{3} \cdot (6 + 3 c)$

Cancel the common factor.

$\frac{1}{8} (8 (- c)) + \frac{1}{8} \cdot 16 - \frac{1}{3} \cdot (6 + 3 c)$

Rewrite the expression.

$- c + \frac{1}{8} \cdot 16 - \frac{1}{3} \cdot (6 + 3 c)$

Cancel the common factor of $8$ .

Factor $8$ out of $16$ .

$- c + \frac{1}{8} \cdot (8 (2)) - \frac{1}{3} \cdot (6 + 3 c)$

Cancel the common factor.

$- c + \frac{1}{8} \cdot (8 \cdot 2) - \frac{1}{3} \cdot (6 + 3 c)$

Rewrite the expression.

$- c + 2 - \frac{1}{3} \cdot (6 + 3 c)$

Apply the distributive property.

$- c + 2 - \frac{1}{3} \cdot 6 - \frac{1}{3} (3 c)$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$- c + 2 + \frac{- 1}{3} \cdot 6 - \frac{1}{3} (3 c)$

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $2$ .

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

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

Factor $3$ out of $3 c$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- c + 2 - 2 - 1 c$

Rewrite $- 1 c$ as $- c$ .

$- c + 2 - 2 - c$

Step 2

Simplify by adding terms.

Combine the opposite terms in $- c + 2 - 2 - c$ .

Subtract $2$ from $2$ .

$- c + 0 - c$

Add $- c$ and $0$ .

$- c - c$

Subtract $c$ from $- c$ .

$- 2 c$

Simplify 1/8(-8c+16)-1/3(6+3c)

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