Question : What is the simplified value of $(2+1)(2^{2}+1)(2^{4}+1)(2^{8}+1)$?
Option 1: $2^{8}-1$
Option 2: $2^{16}-1$
Option 3: $2^{32}-1$
Option 4: $2^{64}-1$
Answer (1)
23rd Jan, 2024
Correct Answer: $2^{16}-1$
Solution :
Given: $(2+1)(2^{2}+1)(2^{4}+1)(2^{8}+1)$
Multiplying (2 – 1) = 1 in the equation, we get:
$(2-1)(2+1)(2^{2}+1)(2^{4}+1)(2^{8}+1)$
= $(2^2-1)(2^{2}+1)(2^{4}+1)(2^{8}+1)$
= $(2^4-1)(2^{4}+1)(2^{8}+1)$
= $(2^8-1)(2^{8}+1)$
= $(2^{16}-1)$
Hence, the correct answer is $(2^{16}-1)$.
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