Question #263149

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

A: (C + D)2

B: 2(C + D)

C: C2 + D2

D: C2 − D2

(10 points)


1
Expert's answer
2021-11-09T16:02:03-0500
C>D>0C>D>0

(C+D)2=C2+2CD+D2>C2+D2(C+D)^2=C^2+2CD+D^2>C^2+D^2



(C+D)2=(C+D)(C+D)>(C+D)(CD)(C+D)^2=(C+D)(C+D)>(C+D)(C-D)

=C2D2=C^2-D^2

(C+D)22(C+D)=(C+D)(C+D2)(C+D)^2-2(C+D)=(C+D)(C+D-2)

Therefore:

If C+D>2,C+D>2, then


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

If C+D<2,C+D<2, then


B:2(C+D)B: 2(C + D)


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