document.write( "Question 1178730: My son is learning factoring polynomials and he has a question that he is confused about. Would appreciate your help in clarifying this.\r
\n" ); document.write( "\n" ); document.write( "During factoring we factor the negative sign of the leading coefficient so why is that not done when we factor a difference of squares like 81 - x^2?\r
\n" ); document.write( "\n" ); document.write( "If written in standard form it would be - x^2 + 81. So why is this incorrect :\r
\n" ); document.write( "\n" ); document.write( " 81-x^2\r
\n" ); document.write( "\n" ); document.write( " - x^2 + 81\r
\n" ); document.write( "\n" ); document.write( "- ( x^2 - 81)\r
\n" ); document.write( "\n" ); document.write( "- ( x + 9 ) ( x-9)\r
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\n" ); document.write( "\n" ); document.write( "His teacher says the correct answer is ( 9 + x) ( 9-x) and NOT -(x+9)(x-9)\r
\n" ); document.write( "\n" ); document.write( "Would appreciate your help. Thank you. \n" ); document.write( "

Algebra.Com's Answer #808113 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Formally,  81-x^2  can be presented / factored as\r\n" );
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document.write( "    81-x^2 = -(x+9)*(x-9).\r\n" );
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document.write( "Formally,  -(x+9)*(x-9)  is IDENTICALLY the same as  (9+x)*(9-x).\r\n" );
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document.write( "So, formally your son's answer is correct.\r\n" );
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document.write( "But  (9+x)*(9-x)  is  traditionally  considered as  \"more simple\"  comparing with  -(x+9)*(x-9).\r\n" );
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\n" ); document.write( "\n" ); document.write( "On these simple factoring formulas, see the lessons\r
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\n" ); document.write( "\n" ); document.write( "1. The square of the sum formula is                  $\"%28a+%2B+b%29%5E2+=+a%5E2+%2B+2ab+%2Bb%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "      For details and examples of applications of this formula see the lesson The square of the sum formula in this site.\r
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\n" ); document.write( "\n" ); document.write( "2. The square of the difference formula is      $\"%28a+-+b%29%5E2+=+a%5E2+-+2ab+%2Bb%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "      For details and examples of applications of this formula see the lesson The square of the difference formula in this site.\r
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\n" ); document.write( "\n" ); document.write( "3. The difference of squares formula is        $\"a%5E2+-+b%5E2+=+%28a+%2B+b%29%2A%28a-+b%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "      For details and examples of applications of this formula see the lesson The difference of squares formula in this site.\r
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