![\"\"](\"/images/stars/stars-13.gif\")
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document.write( "a-[b-c+a-{b-(c-a-a+b)}]\r\n" );
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document.write( "First we look for the innermost grouping symbols, that is,\r\n" );
document.write( "the grouping symbols which have no grouping symbols within them,\r\n" );
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document.write( "I will color them red:\r\n" );
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document.write( "a-[b-c+a-{b-(c-a-a+b)}]\r\n" );
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document.write( "We combine the \"-a-a\" by considering it as \"-1a-1a\" to get \"-2a\",\r\n" );
document.write( "and we replace \"-a-a\" by \"-2a\" and copy everything else over:\r\n" );
document.write( "\r\n" );
document.write( "a-[b-c+a-{b-(c-2a+b)}]\r\n" );
document.write( "\r\n" );
document.write( "Next we remove those innermost grouping symbols by the rule that\r\n" );
document.write( "since it is preceded by a \"-\" sign we drop the grouping symbols by\r\n" );
document.write( "changing all the signs before all the terms. So we replace \r\n" );
document.write( "\"-(c-2a+b)\" by \"-c+2a-b\" and copy everything else over:\r\n" );
document.write( "\r\n" );
document.write( "a-[b-c+a-{b-c+2a-b}]\r\n" );
document.write( "\r\n" );
document.write( "Next we look for the innermost grouping symbols again, that is,\r\n" );
document.write( "the grouping symbols which have no grouping symbols within them,\r\n" );
document.write( "\r\n" );
document.write( "I will color them red:\r\n" );
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document.write( "a-[b-c+a-{b-c+2a-b}]\r\n" );
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document.write( "We see within the { } that thee \"b\" and the \"-b\" add to zero, so\r\n" );
document.write( "we just eliminate them and copy everything else over:\r\n" );
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document.write( "a-[b-c+a-{-c+2a}]\r\n" );
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document.write( "There are no like terms to combine within those grouping symbols,\r\n" );
document.write( "so we remove those grouping symbols again by the rule that since \r\n" );
document.write( "it is preceded by a \"-\" sign we drop the grouping symbols by \r\n" );
document.write( "changing all the signs before all the terms. So we replace \r\n" );
document.write( "\"-{-c+2a}\" by \"+c-2a\" and copy everything else over:\r\n" );
document.write( "\r\n" );
document.write( "a-[b-c+a+c-2a]\r\n" );
document.write( "\r\n" );
document.write( "We see within the [ ] that the \"-c\" and the \"+c\" add to zero, so\r\n" );
document.write( "we just eliminate them and copy everything else over:\r\n" );
document.write( "\r\n" );
document.write( "a-[b+a-2a]\r\n" );
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document.write( "We combine the \"+a-2a\" by considering it as \"+1a-2a\" to get \"-1a\",\r\n" );
document.write( "or just \"-a\" and we replace \"+a-2a\" by \"-a\" and copy everything else \r\n" );
document.write( "over:\r\n" );
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document.write( "a-[b-a]\r\n" );
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document.write( "There are no like terms to combine within those final grouping \r\n" );
document.write( "symbols, so we remove those final grouping symbols again by the rule \r\n" );
document.write( "that since it is preceded by a \"-\" sign we drop the grouping symbols \r\n" );
document.write( "by changing all the signs before all the terms. So we replace \r\n" );
document.write( "\"-[b-a]\" by \"-b+a\" and copy everything else over:\r\n" );
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document.write( "a-b+a\r\n" );
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document.write( "We combine the \"a\" and \"+a\" by considering them as \"1a\" and \"1a\" to get \r\n" );
document.write( "\"2a\" and we replace them by by \"2a\" and copy everything else \r\n" );
document.write( "over, winding up with\r\n" );
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document.write( "2a-b\r\n" );
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document.write( "Edwin \n" );
document.write( "