Question

12 use two different methods to expand \\(\frac{1}{4}(x + 2x + 16 - 8)\\).

Explanation:

Step1 (Method1): Apply distributive property

$\frac{1}{4} \cdot x + \frac{1}{4} \cdot 2x + \frac{1}{4} \cdot 16 - \frac{1}{4} \cdot 8$

Step2 (Method1): Calculate each term

$\frac{1}{4}x + \frac{2}{4}x + 4 - 2 = \frac{3}{4}x + 2$

Step1 (Method2): Combine like terms inside parentheses

$x + 2x + (16 - 8) = 3x + 8$

Step2 (Method2): Multiply by $\frac{1}{4}$

$\frac{1}{4}(3x + 8) = \frac{3}{4}x + 2$

Answer:

$\frac{1}{4}x + \frac{1}{2}x + 4 - 2 = \frac{3}{4}x + 2$ (Method 1: Distributive Property); $\frac{1}{4}(3x + 8) = \frac{3}{4}x + 2$ (Method 2: Combine Like Terms First)