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# What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab

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Director
Joined: 03 Sep 2006
Posts: 789
What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab  [#permalink]

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24 Jan 2012, 08:59
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00:00

Difficulty:

45% (medium)

Question Stats:

71% (01:40) correct 29% (02:14) wrong based on 129 sessions

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What is the value of $$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}$$?

A. a+b-c
B. a-b+c
C. -a+b+c
D. a-b-c
E. -a+b-c
##### Most Helpful Community Reply
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Status: The Best Or Nothing
Joined: 27 Dec 2012
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What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab  [#permalink]

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14 Jul 2014, 21:38
6
1
$$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}$$

This also means that $$a^2+b^2+c^2+ac+bc-ab$$ when multiplied with any one of the 5 options, gives answer $$a^3+b^3-c^3+3abc$$

Just focus on $$a^2, b^2, c^2$$ in the LHS & $$a^3+b^3-c^3$$ on RHS

$$a^2$$ has to be multiplied by "a" to give $$a^3$$

Similarly,$$b^{2} * b = b^3$$

$$c^{2} * -c = -c^3$$

Answer = a+b-c

Answer = A
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Math Expert
Joined: 02 Sep 2009
Posts: 51067
Re: Simplest form of expression  [#permalink]

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24 Jan 2012, 10:26
2
LM wrote:
What is the value of $$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}?$$

A) a+b-c

B) a-b+c

C) -a+b+c

D) a-b-c

E) -a+b-c

Plug-in method would be the most efficient way to deal with this problem.

Let $$a=2$$, $$b=1$$ and $$c=0$$. Then $$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}=3$$. Now let's see which answer choice yields 3:

A. a+b-c=3 --> correct;
B. a-b+c=1 --> discard;
C. -a+b+c=-1 --> discard;
D. a-b-c=1 --> discard;
E. -a+b-c=-1 --> discard.

Answer: A.

P.S. For plug-in method it might happen that for some particular numbers more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.
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Re: What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab  [#permalink]

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01 Dec 2018, 09:17
PareshGmat wrote:
$$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}$$

This also means that $$a^2+b^2+c^2+ac+bc-ab$$ when multiplied with any one of the 5 options, gives answer $$a^3+b^3-c^3+3abc$$

Just focus on $$a^2, b^2, c^2$$ in the LHS & $$a^3+b^3-c^3$$ on RHS

$$a^2$$ has to be multiplied by "a" to give $$a^3$$

Similarly,$$b^{2} * b = b^3$$

$$c^{2} * -c = -c^3$$

Answer = a+b-c

Answer = A

This is such a smart and "simple" approach, kudos mate!
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Re: What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab &nbs [#permalink] 01 Dec 2018, 09:17
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# What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab

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