Question

The side length, s, of a cube is 3x + 2y. If V = s3, what is the volume of the cube?

Answer 1

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  $27x^3+8y^3+54x^2y+36xy^2$

Answer 2

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