document.write( "Question 1025959: Factoirse x^2- (( a+b)^2+a^2/a^2+ab) x+1 \n" ); document.write( "
Algebra.Com's Answer #641253 by Edwin McCravy(20055)\"\" \"About 
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document.write( "\"x%5E2-+%28%28%28a%2Bb%29%5E2%2Ba%5E2%29%2F%28a%5E2%2Bab%29%29x%2B1\"\r\n" );
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document.write( "\"x%5E2-+%28%28%28a%2Bb%29%5E2%2Ba%5E2%29%2F%28a%28a%2Bb%29%29%29x%2B1\" \r\n" );
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document.write( "Since a+b appears twice, let c = a+b \r\n" );
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document.write( "\"x%5E2-+%28%28c%5E2%2Ba%5E2%29%2F%28ac%29%29x%2B1\"\r\n" );
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document.write( "Get a least common denominator of ac\r\n" );
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document.write( "Factor out \"1%2Fac\"\r\n" );
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document.write( "\"expr%281%2Fac%29%28%28ac%29x%5E2-%28a%5E2%2Bc%5E2%29%5E%22%22x%2Bac%29\"\r\n" );
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document.write( "So we try to factorize the trinomial like this,\r\n" );
document.write( "breaking up \"%28ac%29x%5E2\" as the product of \"ax\" and \"cx\":\r\n" );
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document.write( "It doesn't take too much thinking to know that we\r\n" );
document.write( "must fill in the blank spaces with c and a to\r\n" );
document.write( "cause the product to be ac\r\n" );
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document.write( "And if we find the outer and inner products, we\r\n" );
document.write( "find that we get -aČ-bČ which is -(aČ+bČ).\r\n" );
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document.write( "So that is the correct factorization.  All that's\r\n" );
document.write( "left is to substitute (a+b) for c and simplify:\r\n" );
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document.write( "  \r\n" );
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document.write( "Removing the inner parentheses we have:\r\n" );
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document.write( "Edwin

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