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

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

Zepdrix · Answer

Hey Marie :D Remember how to expand a square binomial?
Like this!

$\large\rm (C+D)^2\quad=\quad C^2+2CD+D^2$

Zepdrix · Answer

If we expand out option B we get,
$\large\rm 2(C+D)\quad=\quad 2C+2D$

simplymariex · Answer

Ooh so it's option B?

Zepdrix · Answer

Oh I left you hanging sorry :OOO

Zepdrix · Answer

So this is A after we expand it out,
$\large\rm C^2+2CD+D^2$

And this is C,
$\large\rm C^2+D^2$

Since our values C and D are positive,
you can clearly see how option A is larger, right?
Option C is the same, but it's missing the middle part.

Zepdrix · Answer

It would be easier to leave A in the non-expanded form so we can compare it to option B. So A looks like this,
$\large\rm (C+D)^2$
and B looks like this,
$\large\rm 2(C+D)$

As a general rule, square is going to result in a much much larger number than multiplying by 2.

So therefore option A is larger than option B.

Zepdrix · Answer

And option D is subtraction... so that's going to be a much smaller number.
If they want you to justify it using some math techniques...
you can actually factor option D into conjugates,
$\large\rm C^2-D^2\quad=\quad (C+D)(C-D)$

Which is smaller than option A,
$\large\rm (C+D)^2\quad=\quad (C+D)(C+D)$

Falconmaster · Answer

hey trust this guy ^ he know what he is talking about

SLAYEDQUEEN · Answer

hey sarah