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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

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5 answers to this question

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

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

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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)

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