document.write( "Question 93564: factor completely\r
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Algebra.Com's Answer #68135 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "factor completely \r\n" );
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document.write( "\"z%5E4-81\"\r\n" );
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document.write( "Write \"z%5E4\" as \"%28z%5E2%29%5E2\"\r\n" );
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document.write( "Write \"81\" as \"9%5E2\"\r\n" );
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document.write( "\"%28z%5E2%29%5E2-9%5E2\"\r\n" );
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document.write( "Rule for factoring the difference of two squares:\r\n" );
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document.write( "\"A%5E2-B%5E2\" factors as \"%28A-B%29%28A%2BB%29\"\r\n" );
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document.write( "Here \"A+=+z%5E2\" and \"B=9\"\r\n" );
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document.write( "So answer = \r\n" );
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document.write( "\"%28z%5E2-9%29%28z%5E2%2B9%29\"\r\n" );
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document.write( "But wait! That's not all! That first factor\r\n" );
document.write( "\"z%5E2-9\" is also the difference of two \r\n" );
document.write( "perfect squares, which can be seen if we \r\n" );
document.write( "write the \"9\" as \"3%5E2\"\r\n" );
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document.write( "\"%28z%5E2-3%5E2%29%28z%5E2%2B9%29\" \r\n" );
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document.write( "Then use the same rule again on the first\r\n" );
document.write( "parentheses, this time with \"A=z\" and \"B=3\"\r\n" );
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document.write( "\"%28z-3%29%28z%2B3%29%28z%5E2%2B9%29\"\r\n" );
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document.write( "That's the final answer.  A word of caution. Do not\r\n" );
document.write( "attempt to factor the last factor \"z%5E2%2B9\".  That\r\n" );
document.write( "is the SUM of two squares, which doesn't factor. Only\r\n" );
document.write( "the DIFFERENCE of two squares can be factored.\r\n" );
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document.write( "Edwin
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