Question

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. 2(A + B) (A + B)2 A2 + B2 A2 − B2

Answer 1

Answer:

The value for the expression $(A+B)^{2}$ is the largest

Step-by-step explanation:

Since both A and B must be greater than 0 and A>B then we can assume the least possible values for B=1 and A=2.

So,

i) 2(A+B) = 2(2+1) = 2*3 = 6

ii) $(A+B)^{2}$ = (A+B)*(A+B) = (2+1)*(2+1) = 3*3 = 9

iii) $A^{2} + B^{2}$  = $2^{2} +1^{2}$ = 4+1 = 5

iv) $A^{2} - B^{2} = 2^{2} - 1^{2}$ = 4-1 =3

Inspecting the answers of the above four expressions, we see that the value for the expression $(A+B)^{2}$ is the largest.