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
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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