document.write( "Question 977171:
	        1	1       1\r\n" );
document.write( "Show that       x	y       z      = (y - x)(z-x)(z-y)\r\n" );
document.write( "	        X2     y2      z2

\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #598715 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "We are to show that:\r\n" );
document.write( "\r\n" );
document.write( "\"abs%28matrix%283%2C3%2C1%2C1%2C1%2Cx%2Cy%2Cz%2Cx%5E2%2Cy%5E2%2Cz%5E2%29%29\"\"%22%22=%22%22\"\"%28y+-+x%29%28z-x%29%28z-y%29\"\r\n" );
document.write( "\r\n" );
document.write( "Expand the determinant by the top row:\r\n" );
document.write( "\r\n" );
document.write( "\"1%2Aabs%28matrix%282%2C2%2Cy%2Cz%2Cy%5E2%2Cz%5E2%29%29\"\"%22%22-%22%22\"\"1%2Aabs%28matrix%282%2C2%2Cx%2Cz%2Cx%5E2%2Cz%5E2%29%29\"\"%22%22%2B%22%22\"\"1%2Aabs%28matrix%282%2C2%2Cx%2Cy%2Cx%5E2%2Cy%5E2%29%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"1%2A%28yz%5E2-y%5E2z%29-1%2A%28xz%5E2-x%5E2z%29%2B1%2A%28xy%5E2-x%5E2y%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"yz%5E2-y%5E2z-xz%5E2%2Bx%5E2z%2Bxy%5E2-x%5E2y\"\r\n" );
document.write( "\r\n" );
document.write( "Let's multiply out the right side:\r\n" );
document.write( "\r\n" );
document.write( "\"%28y-x%29%28z-x%29%28z-y%29\"\"%22%22=%22%22\"\"%28y-x%29%28z%5E2-yz-xz%2Bxy%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\"yz%5E2-y%5E2z-xyz%2Bxy%5E2+-+xz%5E2%2Bxyz%2Bx%5E2z-x%5E2y\"\"%22%22=%22%22\"\"%22%22=%22%22\"\"yz%5E2-y%5E2z%2Bxy%5E2+-+xz%5E2%2Bx%5E2z-x%5E2y\"\r\n" );
document.write( "\r\n" );
document.write( "They are the same except for the order of the terms.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );