It is silly to compute .x C y/20 by expanding it to a million terms and then collecting

Chapter 17, Problem 17.34

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It is silly to compute .x C y/20 by expanding it to a million terms and then collecting like terms. A much better way is to calculate .x C y/2 and collect like terms. Then multiply that result by .x C y/ and collect like terms to give .x C y/3 . Now multiply that again by .x C y/ and so on until you reach .x C y/20. Compare this method to the method of generating all of Pascals triangle down to the 20th row

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