How do I evaluate something like 3070^2-3069^2?

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This looks pretty daunting, but the key to this sort of a problem, which has come up a couple of times in previous PAT tests, is to recognise that this expression is actually the difference of two squares. It can be generalised to the problem of evaluating:

x2-y2

which has as its solution:

x2-y2 = (x+y)(x-y)

so in this case:

30702-30692 = (3070+3069)(3070-3069)=(6139)(1)=6139

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