Question

The measure of one side of a cube is represented by the expression 2x+y+3z. What is the volume of the said cube(in expanded form)?

Answer 1

`(2x+y+3z)^3=(2x+y+3z)(2x+y+3z)(2x+y+3z)`

`(2x+y+3z)(2x+y+3z)=4x^2+2xy+6xz+2xy+y^2+3yz+6xz+3yz+9z^2`

=`4x^2+y^2+9z^2+4xy+6yz+12xz`

`(2x+y+3z)[4x^2+y^2+9z^2+4xy+6yz+12xz]`

=`8x^3 +2xy^2+ 18xz^2+8x^2y+12xyz+24x^2z+`

`4x^2y+y^3+9yz^2+4xy^2+6y^2z+12xyz+`

`12x^2z+3y^2z+27z^3+12xyz+18yz^2+36xz^2`

=`8x^3+y^3+27z^3+12x^2y+36xyz+36x^2z+27yz^2+6xy^2+54xz^2+9y^2z`