- #1

CynicusRex

Gold Member

- 98

- 68

This isn't really homework so I wasn't quite sure where to post this. Anyway, I've got a question regarding the following:

"Problem 113. Factor a³-b³.

Solution: The expression a³-b³ has a zero value when a = b. So it is reasonable to expect a factor a - b..."

Now, it is in fact a factor: (a-b)(a²+ab+b²) = a³-b³. So determining the zero value is useful in at least some cases. But when using this method in problem 117; Factor a² - 4b², it doesn't work. We get a zero value when a = 4b, but (a-4b) is not a factor.Solution: The expression a³-b³ has a zero value when a = b. So it is reasonable to expect a factor a - b..."

I noticed it was similar to a²-b² and figured (a+2b)(a-2b) was likely the answer, and it is. However I was curious if the former method would work.

Why doesn't the zero value 'trick' work here?