Question : The sum of $6xy(2x-4z), 3yz(2x-3z)$ and $4xz(3y-2y^2)$ is:
Option 1: $12x^2y-6xyz-9yz^2+8xy^2z$
Option 2: $12x^2y-6xyz+9yz^2-8xy^2z$
Option 3: $12x^2y-6xyz-9yz^2-8xy^2z$
Option 4: $12x^2y+6xyz-9yz^2-8xy^2z$
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Correct Answer: $12x^2y-6xyz-9yz^2-8xy^2z$
Solution :
Given:
$6xy(2x-4z)+ 3yz(2x-3z)$ + $4xz(3y-2y^2)$
= $12x^2y-24xyz+6xyz-9yz^2+12xyz-8xy^2z$
= $12x^2y-6xyz-9yz^2-8xy^2z$
Hence, the correct answer is $12x^2y-6xyz-9yz^2-8xy^2z$.
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