Bunuel wrote:

For all numbers a and b, let a#b = (a + b)^2 – 2ab. Which of the following must be true?

I. x#y = y#x

II. (x#y)#z = (z#x)#y

III. (x + y)#(x – y) = 2(x#y)

A. I

B. II only

C. III only

D. I and III only

E. II and III only

a#b = (a + b)^2 – 2ab

a#b = \(a^2 + b^2\)

I

x#y = \(x^2 + y^2\) = y#x...Stands

II

(x#y)#z = \((x^2+y^2)^2 + z^2\)

(z#x)#y = \((z^2+x^2)^2 + y^2\)

Not equal

III

(x + y)#(x – y) = 2(x#y)

\((x+y)^2 + (x-y)^2 = 2 (x^2 + y^2)\) = 2 (x#y)

I and III

D

_________________

We must try to achieve the best within us

Thanks

Luckisnoexcuse