Question

6 which expressions are equivalent to \\(\frac{1}{5}x(5y + 60)\\)? select all the correct answers. a \\(\frac{1}{5}(2xy + 20x + 3xy + 40x)\\) b \\(xy + 60x\\) c \\(y + 12x\\) d \\(25xy + 300x\\) e \\(13xy\\) f \\(x(y + 12)\\)

Explanation:

Step1: Simplify the original expression

$$\frac{1}{5}x(5y + 60) = \frac{1}{5}x \cdot 5y + \frac{1}{5}x \cdot 60 = xy + 12x$$

Step2: Simplify Option A

$$\frac{1}{5}(2xy + 20x + 3xy + 40x) = \frac{1}{5}(5xy + 60x) = xy + 12x$$

Step3: Simplify Option F

$$x(y + 12) = xy + 12x$$

Step4: Check other options

Option B: $xy + 60x
eq xy + 12x$
Option C: $y + 12x
eq xy + 12x$
Option D: $25xy + 300x
eq xy + 12x$
Option E: $13xy
eq xy + 12x$

Answer:

A. $\frac{1}{5}(2xy + 20x + 3xy + 40x)$
F. $x(y + 12)$