SedateFrog712
  • SedateFrog712
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
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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SedateFrog712
  • SedateFrog712
@Vocaloid im having a bit of trouble understanding the question
Vocaloid
  • Vocaloid
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
Vocaloid
  • Vocaloid
here's a hint: expand (C+D)^2 using FOIL

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More answers

SedateFrog712
  • SedateFrog712
C^2+CD+DC+D^2
Vocaloid
  • Vocaloid
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?
SedateFrog712
  • SedateFrog712
yes i am
Vocaloid
  • Vocaloid
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
SedateFrog712
  • SedateFrog712
ok
Vocaloid
  • Vocaloid
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)
SedateFrog712
  • SedateFrog712
ok
Vocaloid
  • Vocaloid
I'm not sure how detailed of an explanation they want, but hopefully that points you in the right direction
SedateFrog712
  • SedateFrog712
im sure it will be fine thanks for the help you where very thorough and helpful :D

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