Question

write the expanded form of the expression. (\frac{1}{2}(y + 5x)) (\frac{1}{2}(y + 5x) = square) (simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Apply distributive property

The distributive property states that \( \frac{1}{2}(a + b)=\frac{1}{2}a+\frac{1}{2}b \). Here, \( a = y \) and \( b = 5x \). So we have \( \frac{1}{2}(y + 5x)=\frac{1}{2}y+\frac{1}{2}\times5x \).

Step2: Simplify the second term

Calculate \( \frac{1}{2}\times5x \), which is \( \frac{5}{2}x \). So the expanded form is \( \frac{1}{2}y+\frac{5}{2}x \) (or we can also write it as \( \frac{5}{2}x+\frac{1}{2}y \) by rearranging the terms).

Answer:

\( \frac{1}{2}y+\frac{5}{2}x \) (or \( \frac{5}{2}x+\frac{1}{2}y \))