document.write( "Question 1047131: Factor this expression as a difference of squares. a^2+4a-b^2\r
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Algebra.Com's Answer #662644 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "This cannot be factored using only rational expressions, \r\n" );
document.write( "but if you allow square roots in the factorization, then \r\n" );
document.write( "there are more than one way to do this, and each way gives\r\n" );
document.write( "a different expression. \r\n" );
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document.write( "Here's the first way:\r\n" );
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document.write( "\"a%5E2%2B4a-b%5E2\"\r\n" );
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document.write( "Write aČ+4a as its square root squared:\r\n" );
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document.write( "\"%28sqrt%28a%5E2%2B4a%29%29%5E2-b%5E2\"\r\n" );
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document.write( "Then factor it as the difference of two squares:\r\n" );
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document.write( "\"%28sqrt%28a%5E2%2B4a%29-b%29%28sqrt%28a%5E2%2B4a%29%2Bb%29\"\r\n" );
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document.write( "Here's a second way:\r\n" );
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document.write( "\"a%5E2%2B4a-b%5E2\"\r\n" );
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document.write( "Swap the second and third terms:\r\n" );
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document.write( "\"a%5E2-b%5E2%2B4a\"\r\n" );
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document.write( "Factor out a - from the 2nd and 3rd terms:\r\n" );
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document.write( "\"a%5E2-%28b%5E2-4a%29\"\r\n" );
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document.write( "Write the expression in parentheses as the \r\n" );
document.write( "square of its square root:\r\n" );
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document.write( "\"a%5E2-%28sqrt%28b%5E2-4a%29%29%5E2\"\r\n" );
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document.write( "Then factor as the difference of two squares:\r\n" );
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document.write( "\"%28a-sqrt%28b%5E2-4a%29%29%28a%2Bsqrt%28b%5E2-4a%29%29\"\r\n" );
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document.write( "Here's a third way:\r\n" );
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document.write( "\"a%5E2%2B4a-b%5E2\"\r\n" );
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document.write( "Add +4 after the 4a and subtract 4 after the -b^2\r\n" );
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document.write( "\"a%5E2%2B4a%2B4-b%5E2-4\"\r\n" );
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document.write( "Factor the first three terms as a perfect square trinomial.\r\n" );
document.write( "Factor a negative out of the last two terms:\r\n" );
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document.write( "\"%28a%2B2%29%5E2-%28b%5E2%2B4%29\"\r\n" );
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document.write( "Then write the expression in parentheses after the - sign \r\n" );
document.write( "as the square of its square root.\r\n" );
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document.write( "\"%28a%2B2%29%5E2-%28sqrt%28b%5E2%2B4%29%29%5E2\"\r\n" );
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document.write( "Then as\r\n" );
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document.write( "\"%28%28a%2B2%29-sqrt%28b%5E2%2B4%29%29%28%28a%2B2%29%2Bsqrt%28b%5E2%2B4%29%29\"\r\n" );
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document.write( "There are other ways as well, but they'll always involve\r\n" );
document.write( "square roots.  \r\n" );
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document.write( "Edwin

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