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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2
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06 Jun 2017, 13:08
06 Jun 2017, 13:08
1
00:00
Question Stats:
77% (02:07) correct
22% (02:22) wrong based on 27 sessions
Hide Show timer Statistics
\(2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2 - 20^2 =\)
A) -40
B) -110
C) -220
D) -440
E) -880
A) -40
B) -110
C) -220
D) -440
E) -880
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2
[#permalink]
07 Jun 2017, 15:06
07 Jun 2017, 15:06
2
GreenlightTestPrep wrote:
\(2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2 - 20^2 =\)
A) -40
B) -110
C) -220
D) -440
E) -880
A) -40
B) -110
C) -220
D) -440
E) -880
Here's an approach that uses differences of squares
2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² = (2² - 4²) + (6² - 8²) + (10² - 12²) + (14² - 16²) + (18² - 20²)
= (2 - 4)(2 + 4) + (6 - 8)(6 + 8) + (10 - 12)(10 + 12) + (14 - 16)(14 + 16) + (18 - 20)(18 + 20)
= (-2)(2 + 4) + (-2)(6 + 8) + (-2)(10 + 12) + (-2)(14 + 16) + (-2)(18 + 20)
= -2[(2 + 4) + (6 + 8) + (10 + 12) + (14 + 16) + (18 + 20) ]
= -2(6 + 14 + 22 + 30 + 38)
= -2(110)
= -220
Answer: C
Cheers,
Brent
Re: 2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2
[#permalink]
20 Aug 2019, 11:07
20 Aug 2019, 11:07
I imagine it's relatively simple, and I should know it, but can you tell me how this:
(2 - 4)(2 + 4)
became this:
(-2)(2 + 4)
(2 - 4)(2 + 4)
became this:
(-2)(2 + 4)
