Where are the rest?

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Simplify the following: ( x − a ) ( x − b ) ( x − c ) ( x − d ) ⋯ ( x − y ) ( x − z ) (x-a)(x-b)(x-c)(x-d)\cdots(x-y)(x-z) .

x 26 + a b c ⋯ x y z x^{26} + abc\cdots xyz 1 The answer is too large to write 0

Emmanuel John Baliwag by Emmanuel John Baliwag , 21, Philippines

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1 solution

( x − a ) ( x − b ) ( x − c ) ( x − d ) . . . ( x − y ) ( x − z ) (x-a)(x-b)(x-c)(x-d)...(x-y)(x-z)

Expanding it a little bit, we get: ( x − a ) ( x − b ) ( x − c ) ( x − d ) . . . ( x − x ) ( x − y ) ( x − z ) (x-a)(x-b)(x-c)(x-d)...(x-x)(x-y)(x-z)

We all know that ( x − x ) = 0 (x-x) = 0

Any number multiplied to 0 0 is 0 0

Therefore, ( x − a ) ( x − b ) ( x − c ) ( x − d ) . . . ( x − x ) ( x − y ) ( x − z ) (x-a)(x-b)(x-c)(x-d)...(x-x)(x-y)(x-z) ( x − a ) × ( x − b ) × ( x − c ) × ( x − d ) × . . . × 0 × ( x − y ) × ( x − z ) = 0 (x-a)\times(x-b)\times(x-c)\times(x-d)\times... \times 0\times(x-y)\times(x-z) = \boxed{0 }

3 Helpful 0 Interesting 0 Brilliant 0 Confused

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