Factorising problem? with two "squared" brackets

Nov 2011
New Zealand
So here is my math problem - I think it was supposed to be just straightforward factorising, but since it isn't a generic quadratic equation (or maybe it is haha, I can't tell if it is, in this form!) I can't work out how to factorise right down to the answer the book says. Here is the problem.

Factorise the expression
(x - 3)2 - (y - 2)2

The answer is apparently: (x + y - 5)(x - y - 1)

but the only thing I could work out how to do was: (x - 3)(x - 3) - (y - 2)(y - 2)

Please explain how one would reach the correct answer?
Dec 2011
St. Augustine, FL.
Hint: use the difference of squares formula: \(\displaystyle a^2-b^2=(a+b)(a-b)\)
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