Doug C. answered • 07/10/22
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Doug C.
The addition/subtraction of ab^k is just the technique that is used to transform the original expression into the different form in step 2. Think of it similar to multiplying top and bottom of 1/sqrt(2) by sqrt(2)/sqrt(2) to rationalize the denominator. How do we know to do that? Experience? Someone figured it out and made it known? As far as the (a-b). That factor appears in both terms of the expression. It does not disappear from the 2nd term; it is factored out from both terms. like this: If you have something like P(A-B) + Q(A-B), a binomial expression, the factor (A-B) appears in both terms (the terms are separated by a + sign). You can factor out that binomial resulting in (A-B)[P+Q]. That is what happened in step 3.
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07/11/22
Annie N.
My question a) Why do you -ab^k + ab^k in the first step? b) Why is a-b (at the end of second step) cancelled out in the third step?07/11/22