A) \[3\left( x-1 \right)\left( y+2 \right)\left( z-3 \right)\]
B) \[3\left( x+1 \right)\left( y-2 \right)\left( z-3 \right)\]
C) \[3\left( x-1 \right)\left( y-2 \right)\left( z+3 \right)\]
D) \[3\left( x-1 \right)\left( y-2 \right)\left( z-3 \right)\]
Correct Answer: D
Solution :
(d): \[x+y+z=6\] \[\Rightarrow x+y+z-6=0\Rightarrow (x-1)+(y-2)+(z-~3)=0\]\[\therefore {{\left( x-1 \right)}^{3}}+{{\left( y-2 \right)}^{3}}+{{\left( z-3 \right)}^{3}}\] \[~=3\left( x-1 \right)\left( y-2 \right)\left( z-3 \right)\]
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