Question 553040

{{{(r+g)(r^2-r*g+g^2)}}} Start with the given expression.



{{{r(r^2-r*g+g^2)+g(r^2-r*g+g^2)}}} Expand.



{{{(r)*(r^2)+(r)*(-r*g)+(r)*(g^2)+(g)*(r^2)+(g)*(-r*g)+(g)*(g^2)}}} Distribute.



{{{r^3-g*r^2+g^2*r+g*r^2-g^2*r+g^3}}} Multiply.



{{{r^3+g^3}}} Now combine like terms.



 So {{{(r+g)(r^2-r*g+g^2)}}} expands to {{{r^3+g^3}}}.



In other words, {{{(r+g)(r^2-r*g+g^2)=r^3+g^3}}}.



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