How do you solve this problem as quickly as possible? I spent too much time doing this problem. What's the time-efficient way? Thanks.
(2^2 -1)(2^2 +1)(2^4+1)(2^8+1) =
a) 2^16 -1
b) 2^16 +1
c) 2^32 -1
d) 2^128 -1
e) 2^16(2^16 -1)
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Exponent Problem Under 2 min
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ayankm
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This problem utilises the formula (a+b)(a-b) = a^2 - b^2.
(2^2 -1)(2^2 +1)(2^4+1)(2^8+1)
= (2^4 - 1)(2^4 + 1)(2^8+1) --> because (2^2 -1)(2^2 +1) resembles the formula (a+b)(a-b) = a^2 - b^2
= (2^8 - 1)(2^8+1)
= 2^16 - 1.
Ans is Option A.
(2^2 -1)(2^2 +1)(2^4+1)(2^8+1)
= (2^4 - 1)(2^4 + 1)(2^8+1) --> because (2^2 -1)(2^2 +1) resembles the formula (a+b)(a-b) = a^2 - b^2
= (2^8 - 1)(2^8+1)
= 2^16 - 1.
Ans is Option A.
