Question

Can someone guide me through this 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. C2 + D2
D. C2 − D2

Answer 1

@Vocaloid im having a bit of trouble understanding the question

Answer 2

C and D both represent positive numbers (it's not specified, so they can be anything) such that C is bigger than D

it wants you to figure out which of the four answer choices represents the biggest number

Answer 3

here's a hint: expand (C+D)^2 using FOIL

Answer 4

C^2+CD+DC+D^2

Answer 5

good, we can combine that together to get

C^2 + 2CD + D^2

so we know right off the bat that A is bigger than C and D, with me so far?

Answer 6

yes i am

Answer 7

now we compare A and B

A is C^2 + 2CD + D^2
B is 2C + 2D after we apply the distributive property

intuitively, we can guess that A will probably be bigger than B, but we can be sure by testing the most extreme case where C = 2 and D = 1

Answer 8

ok

Answer 9

A = 2^2 + 2(2)(1) + (1)^2 = 4 + 4 + 1 = 9
B = 2(1 + 2) = 6

so even when C and D are at their minimum, A is still bigger than B. as C and D grow larger, the difference between A and B will also grow larger (mainly because of the exponent 2 on C and D)

Answer 10

ok

Answer 11

I'm not sure how detailed of an explanation they want, but hopefully that points you in the right direction

Answer 12

im sure it will be fine thanks for the help you where very thorough and helpful :D