For the rational numbers a, b and c, which of the following is true?

a $\times$ (b + c) = (a + b) $\times$ (a + c)

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a $\times$ (b + c) = (a + b) $\times$ (a + c) = 1

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a $\times$ (b + c) = (a $\times$ b) + (a $\times$ c)

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a $\times$ (b + c) = (a $\times$ b) - (a $\times$ c)

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Solution

The correct option is C
a $\times$ (b + c) = (a $\times$ b) + (a $\times$ c)

Distributive property for three numbers a, b and c is given by,

a $\times$ (b + c) = (a $\times$ b) + (a $\times$ c)

The distributivity is applicable even for rational numbers. It involves sum of the product of two rational numbers.

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a^{2} + b^{2} + c^{2} - a b - b c - c a = 0

a = b = c

{(\sum_{a, b, c} a)}_{a, b, c}^{4} - \sum_{a, b, c} (a + b)^{4} + \sum_{a, b, c} (a)^{4}

\sum_{a, b, c} (a + 1) (a + 2) (b - c)

a + b + c = 0

(\frac{b - c}{a} + \frac{c - a}{b} + \frac{a - b}{c}) (\frac{a}{b - c} + \frac{b}{c - a} + \frac{c}{a - b}) = 9

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