Simplify -4a(1/2b+1/4c+1)

$- 4 a (\frac{1}{2} b + \frac{1}{4} c + 1)$

Step 1

Simplify each term.

Combine $\frac{1}{2}$ and $b$ .

$- 4 a (\frac{b}{2} + \frac{1}{4} c + 1)$

Combine $\frac{1}{4}$ and $c$ .

$- 4 a (\frac{b}{2} + \frac{c}{4} + 1)$

Step 2

Apply the distributive property.

$- 4 a \frac{b}{2} - 4 a \frac{c}{4} - 4 a \cdot 1$

Step 3

Simplify.

Cancel the common factor of $2$ .

Factor $2$ out of $- 4 a$ .

$2 (- 2 a) \frac{b}{2} - 4 a \frac{c}{4} - 4 a \cdot 1$

Cancel the common factor.

$2 (- 2 a) \frac{b}{2} - 4 a \frac{c}{4} - 4 a \cdot 1$

Rewrite the expression.

$- 2 a b - 4 a \frac{c}{4} - 4 a \cdot 1$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 a$ .

$- 2 a b + 4 (- a) \frac{c}{4} - 4 a \cdot 1$

Cancel the common factor.

$- 2 a b + 4 (- a) \frac{c}{4} - 4 a \cdot 1$

Rewrite the expression.

$- 2 a b - a c - 4 a \cdot 1$

Multiply $- 4$ by $1$ .

$- 2 a b - a c - 4 a$