document.write( "Question 1001892: Here is my question:\r
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Algebra.Com's Answer #618972 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%28x-a%29%5E2+%2B+%28x-b%29%5E2+%2B+%28x-c%29%5E2+%2B+x%5E2\" ≟ \"a%5E2+%2B+b%5E2+%2B+c%5E2\"\r\n" );
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document.write( "Two expressions are equal if they differ by zero.  So the procedure \r\n" );
document.write( "we will use is to show that the difference between the two expressions \r\n" );
document.write( "above that we want to show equal, is zero.\r\n" );
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document.write( "So we examine this difference:\r\n" );
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document.write( "Remove the outer parentheses:\r\n" );
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document.write( "\"%28x-a%29%5E2+%2B+%28x-b%29%5E2+%2B+%28x-c%29%5E2+%2B+x%5E2-a%5E2+-+b%5E2+-+c%5E2%29\"\r\n" );
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document.write( "Arrange them so as to have three differences of squares:\r\n" );
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document.write( "\"%28x-a%29%5E2-a%5E2+%2B+%28x-b%29%5E2-b%5E2+%2B+%28x-c%29%5E2-c%5E2+%2Bx%5E2\"\r\n" );
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document.write( "Group the three differences of squares:\r\n" );
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document.write( "Factor the three differences of squares:\r\n" );
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document.write( "Remove the inner parentheses:\r\n" );
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document.write( "\"%28x-a-a%29%28x-a%2Ba%29+%2B++%28x-b-b%29%28x-b%2Bb%29+%2B+%28x-c-c%29%28x-c%2Bc%29%2Bx%5E2\"\r\n" );
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document.write( "Collect like terms:\r\n" );
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document.write( "\"%28x-2a%29%28x%29+%2B++%28x-2b%29%28x%29+%2B+%28x-2c%29%28x%29%2Bx%5E2\"\r\n" );
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document.write( "Distribute to remove the parentheses:\r\n" );
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document.write( "\"x%5E2-2ax+%2B++x%5E2-2bx+%2B+x%5E2-2cx%2Bx%5E2\"\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "\"4x%5E2-2ax+-2bx+-2cx\"\r\n" );
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document.write( "Factor out 2x\r\n" );
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document.write( "\"2x%282x-a-b-c%29\"\r\n" );
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document.write( "Substitute a+b+c for 2x since that is given:\r\n" );
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document.write( "\"%28a%2Bb%2Bc%29%28a%2Bb%2Bc-a-b-c%29\"\r\n" );
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document.write( "The second parenthetical expression becomes 0:\r\n" );
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document.write( "\"%28a%2Bb%2Bc%29%280%29\"\r\n" );
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document.write( "\"0\"\r\n" );
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document.write( "The two original expressions differ by 0 so they are equal.\r\n" );
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document.write( "Edwin
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