- #1
Bavariadude
- 4
- 0
I chose this subject title to get your attention.
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?
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?