(Medal) Suppose A and B represent two different school populations where A B and A and B must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary. (Algebra 2)

A) 2(A + B)
B) (A + B)2
C) A2 + B2
D) A2 − B2

Question

(Medal)  Suppose A and B represent two different school populations where A > B and A and B must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary. (Algebra 2)

A)  2(A + B)
   B)  (A + B)2
   C)  A2 + B2
   D) A2 − B2

janu16 · Answer

A+B)^2 is the largest.  It is A^2+2AB+B^2, which is clearly greater than the last two options.  To compare (A+B)^2 and 2(A+B), we remove one A+B so that we're just comparing A+B and 2.  As A+B must be at least 3 (as both must be positive integers, and one must be greater than the other, leading to a minimum value of A=2, B=1), A+B is greater than 2, and as a result, (A+B)^2 is always the largest.

janu16 · Answer

hope that helps

anonymous · Answer

Yes thanks so much! I really didn't understand what I was doing for this.