Question 599397
{{{(v+p)(v^2-vp+p^2)}}} Start with the given expression.



{{{v(v^2-vp+p^2)+p(v^2-vp+p^2)}}} Expand.



{{{(v)*(v^2)+(v)*(-vp)+(v)*(p^2)+(p)*(v^2)+(p)*(-vp)+(p)*(p^2)}}} Distribute.



{{{v^3-v^2p+vp^2+v^2p-vp^2+p^3}}} Multiply.



{{{v^3+p^3}}} Combine like terms.



So {{{(v+p)(v^2-vp+p^2)}}} fully expands and simplifies to {{{v^3+p^3}}}



In other words, {{{(v+p)(v^2-vp+p^2)=v^3+p^3}}} for all values of 'v' and 'p'