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

Answer:

Option: B is correct

Step-by-step 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 $(A+B)^2$.