Question

Which of the following expressions are equivalent to (x + y) − z ?

A. z + (x + y)

B. x +(y − z)

C. None of the above

Answer 1

`\huge\text{B. $\boxed{x+(y-z)}$}`

First, let's take a look at the terms in the original expression. Since its just addition and subtraction, we can get rid of the parentheses, leaving behind just
`x+y-z`.

As long as an answer is made up of a positive
`x`, a positive
`y`, and a negative
`z`, its correct!

Removing the parentheses in choice A leaves us with
`z+x+y`, which has a positive
`z` rather than a negative
`z`, so it's incorrect.

Removing the parentheses in choice B on the other hand gives us
`x+y-z`, which means it's the correct answer! This is a good example of the associative property of addition in action.