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(3^2+1)(81^2+1)(9^2+1)(3^2−1)=
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18 Feb 2021, 04:25
18 Feb 2021, 04:25
1
Expert Reply
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Question Stats:
80% (01:42) correct
20% (02:15) wrong based on 50 sessions
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\((3^2+1)(81^2+1)(9^2+1)(3^2−1)=\)
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: (3^2+1)(81^2+1)(9^2+1)(3^2−1)=
[#permalink]
18 Feb 2021, 06:05
18 Feb 2021, 06:05
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Carcass wrote:
\((3^2+1)(81^2+1)(9^2+1)(3^2−1)=\)
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - 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
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(3^2+1)(81^2+1)(9^2+1)(3^2−1)=
[#permalink]
18 Feb 2021, 06:15
18 Feb 2021, 06:15
1
Carcass wrote:
\((3^2+1)(81^2+1)(9^2+1)(3^2−1)=\)
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
A. \(81^4+1\)
B. \(9^9−1\)
C. \(3^{16}−1\)
D. \(3^{32}−1\)
E. \(3^{96}+1\)
\((9 + 1) (9^4 + 1) (9^2 + 1) (9 - 1)\)
\((9^2 - 1) (9^2 + 1) (9^4 + 1)\)
\((9^4 - 1) (9^4 + 1)\)
\((9^8 - 1\)
\((3^2)^8 - 1\)
\(3^{16} - 1\)
Hence, option C
