Given expression,
(ab+bc)(ab−bc)+(bc+ca)(bc−ac)+(ca+ab)(ac−ab)
Using the identity,
(a+b)(a−b)=a2−b2,
the given expression can be simplified as
(ab)2−(bc)2+(bc)2−(ac)2+(ac)2−(ab)2
By grouping the like terms, this can be further simplified as follows:
[(ab)2−(ab)2]+[(bc)2−(bc)2]+[(ac)2−(ac)2]=0