If a b c d..... x y z stand for distinct numbers, find the value of (x-a)(x-b)(x-c)..... (x-y )(x-z).

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Solution

(x-a) (x-b) (x-c) (x-d) ( x-e) ...................(x-w) (x-x) (x- y) (x- z)
= (x-a) (x-b) (x-c) ................(x-w) ×0 ×(x-y) (x-z)
=0
because any number muliply by zero will equal to 0 and the term (x-x) = 0

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If A = (x–a) (x–b) (x–c) .............(x–z). Then number of terms in the expansion of (a+A) (b+A) (c+A) ..........(z+A) is

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