Question

One side of a cube has a side length of (2x+3y^2). Which expressions shows the volume of the cube as a polynomial?

Answer 1

`\large\boxed{8x^3+36x^2y^2+54xy^4+27y^6}`

Explanation:

`\text{The formula of a volume of a cube with edge}\ \bold{a}:\\\\V=\bold{a}^3\\\\\text{We have}\ \bold{a}=2x+3y^2.\ \text{Substitute}\\\\V=(2x+3y^2)^3\qquad\text{use}\ (a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\V=(2x)^3+3(2x)^2(3y^2)+3(2x)(3y^2)^2+(3y^2)^3\\\\\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^(nm)\\\\V=2^3x^3+3(2^2x^2)(3y^2)+(6x)(3^2y^((2)(2)))+3^3y^((2)(3))\\\\V=8x^3+36x^2y^2+54xy^4+27y^6`