SOLUTION: If x + y = 12, xy = 27, then find the value of x³ + y³

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Question 473351: If x + y = 12, xy = 27, then find the value of x³ + y³
Answer by Edwin McCravy(20054) About Me  (Show Source):
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if x + y = 12, xy = 27, then find the value of x³ + y³
                           x + y = 12

Raise both sides to the 3rd power (cube both sides)

                        (x + y)³ = 12³

           (x + y)(x + y)(x + y) = 1728

          (x + y)(x² + 2xy + y²) = 1728

x³ + 2x²y + xy² + x²y +2xy² + y³ = 1728

           x³ + 3x²y + 3xy² + y³ = 1728

Factor 3xy out of the two middle terms:

            x³ + 3xy(x + y) + y³ = 1728

We substitute 27 for xy and 12 for x + y

             x³ + 3(27)(12) + y³ = 1728

                   x³ + 972 + y³ = 1728

                         x³ + y³ = 756

Edwin