Question

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: C^2 + D^2
D: C^2 - D^2

Answer 1

⓵
(c + d)²
Expand
c² + 2cd + d²
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⓶
B: 2(C + D)
When c and d are between 0 and 1
2(c + d) > (c + d)²
Example c = 0.2 and d 0.1
2(c+d) = 0.6
(c + d)² = 0.09
When c and d are greater than 1 then
(c + d)² > 2(c + d)
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⓷
C: C^2 + D^2
Since (c + d)² expanded is (c² + d²) + 2cd
c² +-d² is always greater
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⓸
D: C^2 − D^2
Subtracting results in a smaller number
c² +-d² is always greater
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Since a schools population can never be between 0 and 1
The answer that you are supposed to choose is
A: (C + D)² <––––––
However the question is defective and should be changed
from: "C and D must be greater than 0︎⃣"
to: C and D must be greater than 1︎⃣