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: $2^{64} - 1$

Question

Question : What is the simplified value of $(3 + 1) (3^{2} + 1) (3^{4} + 1) (3^{8} + 1) (3^{16} + 1)$ ?
Option 1: $\frac{(3^{32} - 1)}{2}$
Option 2: $\frac{(3^{16} - 1)}{2}$
Option 3: $\frac{(3^{64} - 1)}{2}$
Option 4: $\frac{(3^{128} - 1)}{2}$

8 Views

Answer 1

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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Question : What is the simplified value of (2+1)(22+1)(24+1)(28+1)?Option 1: 28−1Option 2: 216−1Option 3: 232−1Option 4: 264−1

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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: $2^{64} - 1$