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1 solution
Let x = 2 0 1 0 . Then the expression is x 6 − 1 0 6 ( ( x + 1 0 ) 2 − 1 0 x ) ( ( 1 0 x ) 2 − 1 0 0 2 ) ( ( x − 1 0 ) 2 + 1 0 x )
Note that ⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧ ( x + 1 0 ) 2 − 1 0 x = x 2 + 1 0 x + 1 0 0 ( 1 0 x ) 2 − 1 0 0 2 = 1 0 0 ( x 2 − 1 0 0 ) ( x − 1 0 ) 2 + 1 0 x = x 2 − 1 0 x + 1 0 0 x 6 − 1 0 6 = ( x − 1 0 ) ( x 2 + 1 0 x + 1 0 2 ) ( x + 1 0 ) ( x 2 − 1 0 x + 1 0 2 )
The expression becomes ( x − 1 0 ) ( x 2 + 1 0 x + 1 0 2 ) ( x + 1 0 ) ( x 2 − 1 0 x + 1 0 2 ) ( x 2 + 1 0 x + 1 0 0 ) ( 1 0 0 ( x 2 − 1 0 0 ) ) ( x 2 − 1 0 x + 1 0 0 ) = 1 0 0