Evaluate $(a + b) (a - b) + (b + c) (b - c) + (c + a) (c - a)$ .

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Solution

We are given,
$(a + b) (a - b) + (b + c) (b - c) + (c + a) (c - a)$
$= (a^{2} b^{2}) + (b^{2} - c^{2}) + (c^{2} - a^{2})$
$= (a^{2} - a^{2}) + (b^{2} - b^{2}) + (c^{2} - c^{2})$
$= 0$
So, $(a + b) (a - b) + (b + c) (b - c) + (c + z) (c - a)$

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