| If \[m+n=-\,2,\]then the value of\[{{m}^{3}}+{{n}^{3}}-6\,\,mn\]is |
A) \[8\]
B) \[4\]
C) \[-\,\,8\]
D) \[-\,\,4\]
Correct Answer: C
Solution :
| \[{{m}^{3}}+{{n}^{3}}-6\,\,mn\] |
| \[=(m+n)({{m}^{2}}+{{n}^{2}}-mn)-6mn\] |
| \[=(-\,\,2)({{m}^{2}}+{{n}^{2}}-mn)-6mn\] |
| \[=-\,2{{m}^{2}}-2{{n}^{2}}+2mn-6mn\] |
| \[=-\,\,2\,\,({{m}^{2}}+{{n}^{2}}+2mn)\] |
| \[=-\,2\,\,{{(m+n)}^{2}}\] |
| \[=-\,2\,\,{{(-\,2)}^{2}}=-\,2\times 4=-\,8\] |
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