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Multiply following. Assume that x is positive.
(3√x-√y)(2√x-5√y)
Solution
(3√x-√y)(2√x-5√y) =6√x2-15√x√y-2√x√y+5√y2
Note as well that the fourth rule says that we must not have any radicals in the denominator. To get rid of them we will utilize some of the multiplication ideas which we looked at above and the procedure of getting rid of the radicals in denominator is called rationalizing the denominator. Actually that is really what this next set of examples is about. They are actually more examples of rationalizing the denominator instead of simplification examples.
Case 1: Suppose we have two terms 7ab and 3ab. When we multiply these two terms, we get 7ab x 3ab = (7 x 3) a 1 + 1 . b 1 + 1 ( Therefore, x m . x n = x m +
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Let u = sin(x). Then du = cos(x) dx. So you can now antidifferentiate e^u du. This is e^u + C = e^sin(x) + C. Then substitute your range 0 to pi. e^sin (pi)-e^sin(0) =0-0 =0
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