What is the simplified value of $(2 + 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1)$ ?

2^{8} - 1

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2^{16} - 1

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2^{32} - 1

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2^{64} - 1

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Solution

The correct option is B $2^{16} - 1$
$(2 + 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1) = (2 - 1) (2 + 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1) = (2^{2} - 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1)$
$= (2^{4} - 1) (2^{4} + 1) (2^{8} + 1) = (2^{8} - 1) (2^{8} + 1) = 2^{16} - 1$

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