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# (n+k)^2 - 2nk =

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3260
Location: India
GPA: 3.12

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29 Oct 2018, 23:23
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Difficulty:

5% (low)

Question Stats:

98% (00:30) correct 2% (00:11) wrong based on 46 sessions

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$$(n+k)^2 - 2nk =$$

A. $$n^2 + k^2$$
B. $$n^2$$
C. $$0$$
D. $$n^2 - k^2$$
E. $$(n-k)^2$$

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Joined: 15 Feb 2018
Posts: 456

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29 Oct 2018, 23:43
$$(n+k)^2$$
This is a 'square of a sum' quadratic. It follows this formula
$$(n+k)^2$$=$$n^2+2nk+k^2$$

Inserting that back into the equation
$$n^2+2nk+k^2$$-2nk

=$$n^2+2nk-2nk+k^2$$

=$$n^2+k^2$$

A
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4558
GMAT 1: 770 Q49 V46
Re: (n+k)^2 - 2nk =  [#permalink]

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21 Feb 2019, 12:44
Top Contributor
pushpitkc wrote:
$$(n+k)^2 - 2nk =$$

A. $$n^2 + k^2$$
B. $$n^2$$
C. $$0$$
D. $$n^2 - k^2$$
E. $$(n-k)^2$$

My approach would have been the same as that provided by philipssonicare

That said, we can also solve this problem by plugging in values and evaluating

Here's what I mean.

If n = 2 and k = 1, then:
(n + k)² - 2nk = (2 + 1)² - 2(2)(1)
= 3² - 4
= 9 - 4
= 5
So, when n = 2 and k = 1, (n + k)² - 2nk = 5

This means the answer choice that is EQUIVALENT to (n + k)² - 2nk must also equal 5 when n = 2 and k = 1

A. n² + k² = 2² + 1² = 5 PERFECT - keep
B. n² = 2² = 4. No good. We need 5. ELIMINATE.
C. 0 No good. We need 5. ELIMINATE.
D. n² - k² = 2² - 1² = 3. No good. We need 5. ELIMINATE
E. (n - k)² = (2 - 1)² = 1. No good. We need 5. ELIMINATE

By the process of elimination, the correct answer is A

Cheers,
Brent
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Re: (n+k)^2 - 2nk =   [#permalink] 21 Feb 2019, 12:44
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