Question

Suppose A and B represent two different school populations where A>B and A and B must be greater then 0. Which of the following expressions is the largest? Explain why. Show all work necessary.

A:2(A+B)
B:(A+B)^2
C:A^2+B^2
D:A^2-B^2

Answer 1

Option: B is correct

Explanation:

We know that A and B represents two different school populations.

Hence, A and B will be a positive integer.

Also we are given A>B

Since,

`(A+B)^2=A^(2)+B^2+2AB`

⇒
`(A+B)^2>A^2+B^2` ( As 2AB is a positive quantity)

Also
`A^2+B^2>A^2-B^2`

Since an positive quantity
`B^2` added to
`A^2` will make the term greater than an positive quantity
`B^2` subtracted from
`A^2`.

Also
`(A+B)^2>2(A+B)`

(Since
`n^2>2n` for all n>2)

Hence the largest term among all the terms is
`(A+B)^2`.