Suppose x and y represent two different school populations where x > y and x and y must be greater than 0. which of the following expressions is the largest? explain why. show all work necessary.
x2 y2
x2 − y2
2(x y)
(x y)2

Assuming the empty spaces are addition signs, the correct answer is:

(X+Y)²

Explanation:

X²+Y² would be greater than X²-Y² since addition gives a greater result than subtraction.

X²+Y² would be greater than 2(X+Y); this is because 2(X+Y) = 2X+2Y, which will be less than X²+Y², since X>Y.

(X+Y)² = (X+Y)(X+Y). This can be simplified using the distributive property:

X(X)+X(Y)+Y(X)+Y(Y) = X²+XY+YX+Y² = X²+2XY+Y². This is greater than X²+Y².

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)