Carcass wrote:
(32+1)(812+1)(92+1)(32−1)=A.
814+1B.
99−1C.
316−1D.
332−1E.
396+1Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math Book This question tests our ability to recognize a potential
difference of squares.
That is:
(a + b)(a - b) = a² - b²(3² + 1)(81² + 1)(9² + 1)(3² − 1) =
(3² + 1)(3² − 1)(9² + 1)(81² + 1)
=
(9 + 1)(9 − 1)(9² + 1)(81² + 1)
=
(9² − 1)(9² + 1)(81² + 1)
= (81 - 1)(81 + 1)(81² + 1)
= (81² - 1)(81² + 1)
= 81⁴ - 1
Check the answer choices......81⁴ - 1 is not among the answer choices. We'll have to REWRITE our answer...
81⁴ - 1 =
(3⁴)⁴ - 1
= 3¹⁶ - 1
Answer: C