document.write( "Question 403240: how do I factor 4y^2+9z^4?\r
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Algebra.Com's Answer #285168 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
how do I factor 4y^2+9z^4?
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document.write( "That's the sum of two squares, since it can be written:\r\n" );
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document.write( "(2y)² + (3z²)²\r\n" );
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document.write( "Normally you can't factor the sum of two squares.  \r\n" );
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document.write( "In rare cases you can but this time you can't.\r\n" );
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document.write( "If your problem had been\r\n" );
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document.write( "y4 + 4z4\r\n" );
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document.write( "instead you could factor it by adding and subtracting 4y²z²\r\n" );
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document.write( "y4 + 4z4 + 4y²z² - 4y²z²\r\n" );
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document.write( "Rearranging terms:\r\n" );
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document.write( "y4 + 4y²z² + 4z4 - 4y²z²\r\n" );
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document.write( "(y4 + 4y²z² + 4z4) - 4y²z²\r\n" );
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document.write( "(y² + 2z²)² - 4y²z²\r\n" );
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document.write( "[(y² + 2z²) - 2yz][(y² + 2z²) + 2yz]\r\n" );
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document.write( "or\r\n" );
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document.write( "(y² - 2yz + 2z²)(y² + 2yz + 2z²)\r\n" );
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document.write( "But that's an advanced factoring technique, and will\r\n" );
document.write( "not work on the problem you had without using square\r\n" );
document.write( "roots.  So the answer to your problem is \"It is a prime polynomial\".\r\n" );
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document.write( "Edwin
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