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Verified Answer :

V = (3x + 2y)³ = (3x + 2y)(3x + 2y)(3x + 2y)
V = (9x² + 12xy + 4y²)(3x + 2y)
V = 27x³ + 36x²y + 12y²x +18x²y + 24xy² + 8y³
V = 27x³ + 54x²y + 36y²x + 8y³

Answer:

\(27x^3+8y^3+54x^2y+36xy^2\)

Explanation:

We have given with a cube whose side is \(3x+2y\) and we need to find  the volume of a cube

Whose volume is defined by \(v=s^3\)

So, according to the formula we will get

\((3x+2y)^3\)

Using the fomula

\((a+b)^3=a^3+b^3+3a^2b+3ab^2\)

Here a=3x and b=2y substituting in the formula we will get

\((3x+2y)^3=(3x)^3+(2y)^3+3(3x)^2(2y)+3(3x)(2y)^2\)

After simplification we will get

\(27x^3+8y^3+54x^2y+36xy^2\)

Hence, volume of cube is  \(27x^3+8y^3+54x^2y+36xy^2\)

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