I chose this subject title to get your attention.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: The curious case of 50x^2 - 72

**Physics Forums | Science Articles, Homework Help, Discussion**