Respuesta :
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
V = (9x² + 12xy + 4y²)(3x + 2y)
V = 27x³ + 36x²y + 12y²x +18x²y + 24xy² + 8y³
V = 27x³ + 54x²y + 36y²x + 8y³
Answer:
[tex]27x^3+8y^3+54x^2y+36xy^2[/tex]
Explanation:
We have given with a cube whose side is [tex]3x+2y[/tex] and we need to find the volume of a cube
Whose volume is defined by [tex]v=s^3[/tex]
So, according to the formula we will get
[tex](3x+2y)^3[/tex]
Using the fomula
[tex](a+b)^3=a^3+b^3+3a^2b+3ab^2[/tex]
Here a=3x and b=2y substituting in the formula we will get
[tex](3x+2y)^3=(3x)^3+(2y)^3+3(3x)^2(2y)+3(3x)(2y)^2[/tex]
After simplification we will get
[tex]27x^3+8y^3+54x^2y+36xy^2[/tex]
Hence, volume of cube is [tex]27x^3+8y^3+54x^2y+36xy^2[/tex]
