The side length, s , of a cube is 3 x plus 2 y If cap v is equal to s cubed , what is the volume of the cube?
Answer
A
27 x cubed plus 54 x squared y plus 36 x y squared plus 8 y cubed
B
27 x cubed plus 54 x squared y plus 18 x y squared plus 2 y cubed
C
3 x cubed plus 18 x squared y plus 36 x y squared plus 8 y cubed
D
27 x cubed plus 18 x squared y plus 12 x y squared plus 2 y cubed
Explanation
The cube’s volume is its side length cubed: V = (3x + 2y)³. Using (a + b)³ = a³ + 3a²b + 3ab² + b³ gives 27x³ + 54x²y + 36xy² + 8y³. This matches choice C.
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