A game consists of rolling two die, one die with six sides, the other die with eight

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A game consists of rolling two die, one die with six sides, the other die with eight sides, and adding the scores together. Both die are fair, with the first numbered 1 to 6 and the second numbered 1 to 8. Show that the probability generating function of Z, where Z is the sum of the scores on the two die, is: 

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