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Anyway, I know how to solve it; it's obviously a matter of factoring and the difference of two squares:

50x^2 - 72

2(25x^2 - 36)

2(5x - 6) (5x + 6)

However, when I try to solve it the normal way -- by factoring -- things go wrong:

50x^2 - 72

2(25x^2 - 36)

2(25x^2 - 450x + 450x - 36)

Here is where things get messy. I can't seem to factor it all the way down to 2(5x - 6) (5x + 6):

2(5x[5x - 90] +3[150x - 12])

If I go for the greatest common factor, I get this:

2(25x[x - 18] +6[75x - 6])

And if I pick a suitable factor, I get this:

2(5x[5x - 90] +6[75x - 6])

In the last one, I was able to form (5x +6), but here's where things come to a dead end.

What confuses me is that if we take a similar problem that can be solved smoothly through the difference of two squares, like, 4x^2 - 9 -- which immediately becomes (2x - 3) (2x + 3) -- it can still be solved through plain factoring:

4x^2 - 9

4x^2 - 6x + 6x - 9

2x(2x - 3) +3(2x - 3)

(2x - 3) (2x + 3)

So why is the straightforward factoring method succeeding with 4x^2 - 9, but failing with 50x^2 - 72?

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# The curious case of 50x^2 - 72

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