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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


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 26th Jan, 2024

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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