Question 133109


{{{(r+p)(r^2-rp+p^2)}}} Start with the given expression




{{{r(r^2-rp+p^2)+p(r^2-rp+p^2)}}} Expand the expression. Remember something like {{{(a+b)(c+d+e)}}} expands to {{{a(c+d+e)+b(c+d+e)}}}



{{{(r)*(1r^2)+(r)*(-1rp)+(r)*(1p^2)+(p)*(1r^2)+(p)*(-1rp)+(p)*(1p^2)}}} Distribute



{{{r^3-r^2p+rp^2+pr^2-p^2r+p^3}}} Multiply



{{{r^3+p^3}}} Combine like terms




So {{{(r+p)(r^2-rp+p^2)}}} expands and simplifies to {{{r^3+p^3}}}.


In other words, {{{(r+p)(r^2-rp+p^2)=r^3+p^3}}}