Respuesta :

The volume of the cube is 27x³ + 8y³ +54x²y + 36xy².

Volume of cube

The volume of a cube is the cube of its side.

[tex]\rm{ Volume\ of\ cube = (side)^3[/tex]

Given to us

  • side length, s = (3x+2y)
  • Volume, V = s³

Algebraic Identity

[tex](a+b)^3= a^3 +b^3 +3a^2b+3ab^2[/tex]

The volume of the cube

[tex]\begin{aligned}Volume &= s^3\\&= (3x+2y)^3\end{aligned}[/tex]

Applying algebraic Identity,

            [tex]=(3x+2y)^3\\\\ =(3x)^3+(2y)^3+[3\times (3y)^2 \times2y]+[3 \times 3x \times(2y)^2]\\\\= 27x^3 + 8y^3 +54x^2y +36xy^2[/tex]          

Hence, the volume of the cube is 27x³ + 8y³ +54x²y + 36xy².

Learn more about Algebraic Identity:

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