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

[Utkrisht123]

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 March 24, 2013 by Utkrisht123

[bonanova]

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

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

[James33]

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

[Prime]

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)

[vinay.singh84]

a² - b²

(a + b - b)² - b²

(a + b)² + b² - 2b(a + b) - b²

(a + b)² - 2b(a + b)

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

(a + b)(a - b)

[Perhaps check it again]

In post # 1 in the right-hand column under

"a^2 - b^2,"

the next line should be

"a^2 + b^2 + 2ab - 2ab - 2b^2."

Edited January 26, 2014 by Perhaps check it again