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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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What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab [#permalink]  24 Jan 2012, 08:59
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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
[Reveal] Spoiler: OA
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Re: Simplest form of expression [#permalink]  24 Jan 2012, 10:26
Expert's post
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;

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]  14 Jul 2014, 15:51
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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]  14 Jul 2014, 21:38
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$$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}$$

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

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

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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] 14 Jul 2014, 21:38
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