If $a + b + c = 0$ , then find the value of $(a + b) (b + c) (c + a) .$

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Solution

Finding the value of expression
We have: $a + b + c = 0$
Therefore, we can write,
$(a + b) = - c . . . . (1) (b + c) = - a . . . . (2) (c + a) = - b . . . . (3)$
On adding equation (1), (2), and (3), we get
The value of $(a + b) (b + c) (c + a) = (- c) (- a) (- b) = - a b c$ .
Hence, The value of $(a + b) (b + c) (c + a)$ is $- a b c .$

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