Question 112005

{{{(2r-3s)(4r^2+6rs+9s^2)}}} Start with the given expression




{{{2r(4r^2+6rs+9s^2)-3s(4r^2+6rs+9s^2)}}} Expand the expression. Remember for something like {{{(a+b)(c+d+e)}}} it expands to {{{a(c+d+e)+b(c+d+e)}}}



{{{(2r)*(4r^2)+(2r)*(6rs)+(2r)*(9s^2)+(-3s)*(4r^2)+(-3s)*(6rs)+(-3s)*(9s^2)}}} Distribute



{{{8r^3+12rs+18rs^2-12sr^2-18s^2r-27s^3}}} Multiply



{{{8r^3+12rs-12r^2s-27s^3}}} Combine like terms



{{{8r^3-12r^2s+12rs-27s^3}}} Sort the terms




So {{{(2r-3s)(4r^2+6rs+9s^2)}}} expands and simplifies to {{{8r^3-12r^2s+12rs-27s^3}}}.


In other words, {{{(2r-3s)(4r^2+6rs+9s^2)=8r^3-12r^2s+12rs-27s^3}}}