A) \[0\]
B) \[3xyz\]
C) \[-\,3xyz\]
D) \[{{z}^{3}}\]
Correct Answer: A
Solution :
[a] Given, \[x+y=z\] \[\therefore \] \[x+y+(-z)=0\] We know that, if \[a+b+c=0\]then \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\] Here,\[x+y+(-z)=0\] \[\therefore \] \[{{x}^{3}}+{{y}^{3}}-{{z}^{3}}=3xy\,(-z)\] \[\Rightarrow \] \[{{x}^{3}}+{{y}^{3}}-{{z}^{3}}+3xyz\] |
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