Question

write the expanded form of the expression.
$\frac{1}{2}(y - x)$
$\frac{1}{2}(y - x)=\square$
(use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Apply the distributive property

The distributive property states that \( a(b - c)=ab - ac \). Here, \( a = \frac{1}{2} \), \( b = y \), and \( c = x \). So we distribute \( \frac{1}{2} \) to both \( y \) and \( -x \) inside the parentheses.
\( \frac{1}{2}(y - x)=\frac{1}{2}\times y-\frac{1}{2}\times x \)

Step2: Simplify the terms

Simplifying the products, we get \( \frac{1}{2}y-\frac{1}{2}x \), which can also be written as \( -\frac{1}{2}x+\frac{1}{2}y \) or \( \frac{1}{2}(-x + y) \), but the expanded form by distributing is \( \frac{1}{2}y-\frac{1}{2}x \) (or rearranged as \( -\frac{1}{2}x+\frac{1}{2}y \)).

Answer:

\( \frac{1}{2}y-\frac{1}{2}x \) (or equivalent forms like \( -\frac{1}{2}x+\frac{1}{2}y \))