Alg_Complete

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Unformatted text preview: 6 = 36 = ( 4 )( 9 ) = 4 9 = ( 2 )( 3) = 6 In other words, we can break up products under a square root into a product of square roots provided both numbers are positive. It turns out that we can actually do the same thing if one of the numbers is negative. For instance, 6i = -36 = ( -4 )( 9 ) = -4 9 = ( 2i )( 3) = 6i However, if BOTH numbers are negative this won’t work anymore as the following shows. 6 = 36 = ( -4 )( -9 ) ¹ -4 -9 = ( 2i )( 3i ) = 6i 2 = -6 We can summarize this up as a set of rules. If a and b are both positive numbers then, © 2007 Paul Dawkins 56 http://tutorial.math.lamar.edu/terms.aspx College Algebra a b = ab - a b = - ab a -b = - ab ( -a )( -b ) - a -b ¹ Why is this important enough to worry about? Consider the following example. Example 4 Multiply the following and write the answer in standard form. 2 - -100 1 + -36 ( )( ) Solution If we where to multiply this out in its present form we would get, (2 - )( ) -100 1 + -36 = 2 + 2 -36 - -100 - -36 -100 Now, if we were not being careful we would probably combine the two roots...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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