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Which of the following is equal to (x – 2)2 + (x – 1)2 + x2

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GMAT Club Legend
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Joined: 07 Jun 2014
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Which of the following is equal to (x – 2)2 + (x – 1)2 + x2 [#permalink] New post 17 Jul 2018, 11:58
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Question Stats:

81% (01:18) correct 18% (01:11) wrong based on 11 sessions
Which of the following is equal to \((x - 2)^2 + (x - 1)^2 + x^2 + (x + 1)^2 + (x + 2)^2\)?

(A) \(5x^2\)
(B) \(5x^2 + 10\)
(C) \(x^2 + 10\)
(D) \(5x^2 + 6x + 10\)
(E) \(5x^2 - 6x + 10\)
[Reveal] Spoiler: OA

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Re: Which of the following is equal to (x – 2)2 + (x – 1)2 + x2 [#permalink] New post 18 Jul 2018, 12:43
sandy wrote:
Which of the following is equal to \((x - 2)^2 + (x - 1)^2 + x^2 + (x + 1)^2 + (x + 2)^2\)?

(A) \(5x^2\)
(B) \(5x^2 + 10\)
(C) \(x^2 + 10\)
(D) \(5x^2 + 6x + 10\)
(E) \(5x^2 - 6x + 10\)



Given

\((x - 2)^2 + (x - 1)^2 + x^2 + (x + 1)^2 + (x + 2)^2\)

It's better to assign value for x. Smaller value.

Let the value of x be 1.

( 1 - 2 )^2 + (1 -1)^2 + (1)^2 + (1+1)^2 + (1+ 2)^2

= 1 + 0 + 1 + 4 + 9

= 15.

Option B:

5x^2 + 10

= 5*1 + 10

= 15.

When we have variable in the answer choice and in question , inserting same value for both cases will help a lot.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1653 [0], given: 396

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Re: Which of the following is equal to (x – 2)2 + (x – 1)2 + x2 [#permalink] New post 28 Jul 2018, 16:13
Expert's post
Explanation

First, multiply out (remember FOIL = First, Outer, Inner, Last) each of the terms in parentheses:

\((x^2 - 2x - 2x + 4) + (x^2 - 1x - 1x + 1) + (x^2) + (x^2 + 1x + 1x + 1) + (x^2 + 2x + 2x + 4)\)

Note that some of the terms will cancel each other out (e.g., –x and x, –2x and 2x):

\((x^2 + 4) + (x^2 + 1) + (x^2) + (x^2 + 1) + (x^2 + 4)\)

Finally, combine:
\(5x^2 + 10\)
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Re: Which of the following is equal to (x – 2)2 + (x – 1)2 + x2   [#permalink] 28 Jul 2018, 16:13
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