Question

prove this (a-b )(a+b)+(b-c)(b+c)+(c-a)(c+a)=o

Answer 1

hope this will help you.

Answer 2

We know that,
$(x + y)(x - y) = x {}^{2} - y {}^{2}$

By using above formula...

Given,
$(a - b)(a + b) + (b - c)(b + c) +( c - a)(c + a) \\ = ( a {}^{2} - b {}^{2}) + (b {}^{2} - c {}^{2}) + ( c {}^{2} - a {}^{2} )\\ = a {}^{2} - b {}^{2} + b {}^{2} - c {}^{2} + c {}^{2} - a {}^{2} \\ = 0$
Hence,
$(a - b)(a + b) + (b - c)(b + c) + (c - a)(c + a) = 0$