Quadratics - Men And Women In Choir Question

[JeffreyB581]

This question popped in my head when the below questions came up in a CAT. It is not specific to the question below but relates to it do to the sum of squares/difference of squares.

When dealing with regular quadratics you must move everything to one side before factoring (zero factor property) but when dealing with special products there is no need? (i.e. in statement 1 you move the -9 to the right side of the equation before factoring the difference of squares).

If there are x men and y women in a choir, and there are z more men than there are women in that choir, what is z?

(1) x2 – 2xy + y2 – 9 = 0

(2) x2 + 2xy + y2 – 225 = 0

Answer is A btw.

[RonPurewal]

well, those aren't "differences of squares". (a "difference of squares" would be exactly what the words say—it'd be one square minus another square. x^2 – y^2, kinda thing.)
but, that's just terminology, which has no particular importance for this exam.

the point—as always—is that you should just try stuff.
if the first thing you try doesn't work ... try other stuff.

it's a BIG mistake to try to construct some huge decision tree that you have to plod through before even starting to solve the problem.
really, just throw stuff at the problem and see whether it works. if it doesn't work, you should come to that realization VERY quickly, and then you can just ... try other stuff.