Jump to content
BrainDen.com - Brain Teasers
  • 0
Utkrisht123

a^2 -b^2 = (a+b)(a-b)

Question

All of you know that a2 - b2 = (a+b)(a-b)

I know only two method to prove it.

a2 - b2 a2 - b2

a2 - b2 + ab - ab a2 - b2 + 2ab -2ab -2b2

a2 + ab - ab - b2 (a+b)2 - 2b(a+b)

a(a+b) - b(a+b) (a+b)(a+b) - 2b(a+b)

(a-b)(a+b) (a+b)(a+b-2b)

(a+b)(a-b)

Apart form these two method are there any other method to prove it.

Edited by Utkrisht123

Share this post


Link to post
Share on other sites

5 answers to this question

  • 0

Can't you prove it just by expanding the product?

All the steps are reversible, so going either direction accomplishes the same thing.

Share this post


Link to post
Share on other sites
  • 0

Perhaps, OP is looking for this:

Suppose, a = b + k, then k = a - b.


a2 - b2 = (b+k)2 - b2 = b2 + 2bk + k2 - b2= k(2b+k) = k(b+k+b)=(a-b)(a+b)

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now


  • Recently Browsing   0 members

    No registered users viewing this page.

×