\(\eqalign{
& \left( {a + b} \right)({a^2} - ab + {b^2}) \cr
& = a({a^2} - ab + {b^2}) + b({a^2} - ab + {b^2}) \cr
& = a.{a^2} + a.\left( { - ab} \right) + a.{b^2} + b.{a^2} + b.\left( { - ab} \right) + b.{b^2} \cr
& = {a^3} - {a^2}b + a{b^2} + {a^2}b - a{b^2} + {b^3} \cr
& = {a^3} + \left( {{a^2}b - {a^2}b} \right) + \left( {a{b^2} - a{b^2}} \right) + {b^3} \cr
& = {a^3} + {b^3} \cr} \)
