The side length, s , of a cube is x minus 2 y If cap v is equal to s cubed , what is the volume of the cube?
Answer
A
x cubed plus 6 x squared y plus 12 x y squared plus 8 y cubed
B
3 x cubed plus 6 x squared y plus 12 x y squared plus 24 y cubed
C
3 x cubed minus 6 x squared y plus 12 x y squared minus 24 y cubed
D
x cubed minus 6 x squared y plus 12 x y squared minus 8 y cubed
Explanation
The volume is the side length cubed, so substitute s = x − 2y to get V = (x − 2y)³. Using the binomial expansion, (a − b)³ = a³ − 3a²b + 3ab² − b³, with a = x and b = 2y, gives x³ − 6x²y + 12xy² − 8y³. This matches choice D.
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