Cube of difference of two numbers remains same if we interchange the numbers.

True

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False

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Solution

The correct option is B
False

Let the two numbers be $a$ and $b$ .

So, $(a - b)^{3} = a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}$ ... (i)

After interchanging the numbers, $(b - a)^{3} = b^{3} - a^{3} - 3 a b^{2} + 3 a^{2} b$ ... (ii)

Take $(-)$ sign common in equation (ii), we get

$(b - a)^{3} = - (- b^{3} + a^{3} + 3 a b^{2} - 3 a^{2} b) = - (a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}) = - (a - b)^{3}$

$\Rightarrow (a - b)^{3} = - (b - a)^{3}$

Thus, the given statement is false

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