help !!

Hmna wrote:If x+2y=a , and x-2y=b, which of the following is an expression for xy?

A)2(a+b/a-b)
b)2(a-b/a+b)
c)1
d)non

Need to point out that usually there are 5 choices in the test. None is usually (E). Also double check if the question asks xy or x/y.


x+2y = a
x-2y = b

Add equations:
==> x=(a+b)/2

Subtract equations
==> y = (a-b)/4

xy = (a^2-b^2)/8

Since we've got

x + 2y = a
x - 2y = b

we know that a = b + 4y, or a - b = 4y

Likewise, adding the two equations together, we know that a + b = (x + 2y) + (x - 2y) = 2x

So we can now replace (a + b) with 2x and (a - b) with 4y.

Working with the answers, this gives us:

(A) 2 * (a + b)/(a - b) => 2 * 2x/4y => 4x/4y = x/y

Not right!

How about (B)?

2 * (a - b)/(a + b) => 2 * 4y / 2x => 4y/x

Nope!

(C) would work if y = 1/x, but we saw above that that isn't the case.

From there, we're left with the disappointing (D).