Question : What is the simplified form of the expression (1 + x) (1 + x2) (1 + x4) (1 + x8) (1 - x)?
Option 1: 1 – x40
Option 2: 1 – x32
Option 3: 1 – x16
Option 4: 1 – x42
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Correct Answer: 1 – x 16
Solution : Given expression, (1 + x) (1 + x 2 ) (1 + x 4 ) (1 + x 8 ) (1 – x) = (1 − x 2 )(1 + x 2 )(1 + x 4 )(1 + x 8 ) = (1 − x 4 )(1 + x 4 )(1 + x 8 ) = (1 − x 8 )(1 + x 8 ) = (1 − x 16 ) Hence, the correct answer is (1 − x 16 ).
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