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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
Joined: 07 Jun 2014
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Which of the following is equal to (x – 2)2 + (x – 1)2 + x2 [#permalink]  17 Jul 2018, 11:58
Expert's post
00:00

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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Sandy
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Manager
Joined: 06 Jun 2018
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Kudos [?]: 56 [0], given: 0

Re: Which of the following is equal to (x – 2)2 + (x – 1)2 + x2 [#permalink]  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
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

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

Re: Which of the following is equal to (x – 2)2 + (x – 1)2 + x2 [#permalink]  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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Sandy
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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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