1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Factoring trick by determining a zero value

  1. Dec 16, 2016 #1


    User Avatar
    Gold Member

    I'm currently working through the book Algebra by I.M. Gelfand and A. Shen on my own. (As advised here: https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/#toggle-id-1)
    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.
    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?
  2. jcsd
  3. Dec 16, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You mean ##a=2b##.
  4. Dec 16, 2016 #3


    User Avatar
    Gold Member

    Ooooh I see my mistake. 4b² ≠ (4b)²
    If I substitute a with 4b, I get (4b)² which is 16b².


    PS I guess this should've been posted in the homework section then.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted