(a + b) (a - b) + (b - c) (b + c) + (c + a) (c - a) is equal to:

1. 2a² + 2b² + 2c²

2. a² + b² + c² - 2ab - 2bc - 2ca

3. 0

4. none of these

[(a + b) (a - b)] + [(b - c) (b + c)] + [(c + a) (c - a)]

Using the formula,

[∵ (x + y)(x - y) = x² - y²]

= [a² - b²] + [b² - c²] + [c² - a²]

= a² - b² + b² - c² + c² - a²

= (a² - a²) + (- b² + b²) + (- c² + c²)

= 0

Hence, option 3 is the correct option.