document.write( "Question 1055888: Evaluate a^3-b^3 when a-b =2 and a^2+b^2=4. \n" ); document.write( "

Algebra.Com's Answer #671055 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "Evaluate a^3-b^3 when a-b =2 and a^2+b^2=4.
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document.write( "Take a-b = 2 and square both sides.\r\n" );
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document.write( "You will get\r\n" );
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document.write( "a^2 - 2ab + b^2 = 4.\r\n" );
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document.write( "Replace here (a^2 + b^2) by 4 (according to the condition).\r\n" );
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document.write( "You will get\r\n" );
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document.write( "4 - 2ab = 4.\r\n" );
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document.write( "It implies ab = 0.\r\n" );
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document.write( "Now a^3 - b^3 = (a-b)*(a^2 +ab + b^2) (standard decomposition/factoring).\r\n" );
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document.write( "Now replace here a-b by 2; replace a^2+b^2 by 4 and replace ab by 0.\r\n" );
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document.write( "You will get\r\n" );
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document.write( "a^3 - b^3 = 2*(4 + 0) = 8.\r\n" );
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document.write( "Answer.  Then  a^3 - b^3 = 8.\r\n" );
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