How solve for Whole Cube equations

[Mack1982]

Hi,
My question is that what is the formula to open a whole cube equation.


(ka+kb+kc)^3
Where a,b,c = variables
And K = Constants

[Dotty-Notation]

Prepare for somthing ugly, since i'm taking it VERY slowly
I'm going to do it for (a+b+c)^3 (just plug kx for a, and so forth, this is a much better way of writing it)

(a+b+c)^3
=((a+b+c)^2)(a+b+c)
=(a+b)^2+2(a+b)c+c^2)(a+b+c)
=(a^2+2ab+b^2+2ac+2bc+c^2)(a+b+c)
=(a^2+2ab+b^2+2ac+2bc+c^2)(a+b)+c(a^2+2ab+b^2+2ac+ 2bc+c^2)
=a(a^2+b^2+c^2+2ab+2ac+2bc)+b(a^2+b^2+c^2+2ab+2ac+ 2bc)+c(a^2+b^2+c^2+2ab+2ac+2bc)
=a^3+b^3+c^3+3(a^2)b+3(a^2)c+3(b^2)a+3(b^2)c+3(c^2 )a+3(c^2)b+6abc

Fun eh?

[Mr. Robin Parsons]

© Mr. Robin Parsons :cool: Kingston Ontario Canada MMVI

Prepare for somthing ugly, since i'm taking it VERY slowly
I'm going to do it for (a+b+c)^3 (just plug kx for a, and so forth, this is a much better way of writing it)

(a+b+c)^3
=((a+b+c)^2)(a+b+c)
=(a+b)^2+2(a+b)c+c^2)(a+b+c)
=(a^2+2ab+b^2+2ac+2bc+c^2)(a+b+c)
=(a^2+2ab+b^2+2ac+2bc+c^2)(a+b)+c(a^2+2ab+b^2+2ac+ 2bc+c^2)
=a(a^2+b^2+c^2+2ab+2ac+2bc)+b(a^2+b^2+c^2+2ab+2ac+ 2bc)+c(a^2+b^2+c^2+2ab+2ac+2bc)
=a^3+b^3+c^3+3(a^2)b+3(a^2)c+3(b^2)a+3(b^2)c+3(c^2 )a+3(c^2)b+6abc

Fun eh?.....except for that missing (and/or extra??) bracket......)