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Question

Find the cube of 3x - 2y - 4z

A
27x354x2y+36xy28y3108x2z+144xyz48y2z+144xz296yz264z3
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B
81x354x2y+36xy28y3108x2z+144xyz48y2z+169xz296yz227z3
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C
81x3+54x2y+36xy28y3108x2z+27xyz48y2z+169xz296yz227z3
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D
27x3+54x2y+36xy2+8y3+108x2z+144xyz48y2z+144xz296yz264z3
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Solution

The correct option is A 27x354x2y+36xy28y3108x2z+144xyz48y2z+144xz296yz264z3
(a+b)3=a3+b3+3ab(a+b)

So if a=3x-2y and b=-4z we get

(3x2y)312z(3x2y)2+48z2(3x2y)64z3

(3x2y)3=27x354x2y+36xy28y3and(3x2y)2=9x212xy+4y2

(3x2y4z)3=27x354x2y+36xy28y3108x2z+144xyz48y2z+144xz296yz264z3.

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