document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28775>Question 28775</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!  I'm making my way through a book called \"The Mathematics of Games and Gambling\" by Edward Packel.  There's an algebraic equation therein which goes like this:<BR>\n" );
document.write( "           x=4pq-5(1-q)-2(1-p)q+3(1-p)(1-q).  The author partially reduces this expression to the following:  <BR>\n" );
document.write( "                                  x=14pq-8p-5q+3.  I don't understand how he arrived at that point.  Using my own highly dodgy math skills, I came up with the following:<BR>\n" );
document.write( "                x=9pq-5p+2q-2.  I tried the \"collecting like terms\" operation, but I obviously veered off the right path somewhere.  Could someone show me the light here, please?  With many thanks, RR </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15789 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OH! MY DEAR !! I THINK YOU MADE A SIMPLE MISTAKE IN COPYING PROBABLY..SEE BELOW<BR>\n" );
document.write( "Hello! I'm making my way through a book called \"The Mathematics of Games and Gambling\" by Edward Packel. There's an algebraic equation therein which goes like this:<BR>\n" );
document.write( "x=4pq-5(1-q)-2(1-p)q+3(1-p)(1-q).<BR>\n" );
document.write( "I THINK YOU MISSED P IN THE SECOND TERM .I PUT IN CAPITAL LETTER IN BRACKETS.IT SHOULD BE <BR>\n" );
document.write( "x=4pq-5(P)(1-q)-2(1-p)q+3(1-p)(1-q)...SO NOW WE GET <BR>\n" );
document.write( "X=4PQ-5P+5PQ-2Q+2PQ+3-3P-3Q+3PQ<BR>\n" );
document.write( "=14PQ-8P-5Q+3...OK.....\r<BR>\n" );
document.write( "\n" );
document.write( " The author partially reduces this expression to the following: <BR>\n" );
document.write( "x=14pq-8p-5q+3. <BR>\n" );
document.write( "OK......SAME AS ABOVE<BR>\n" );
document.write( "I don't understand how he arrived at that point. Using my own highly dodgy math skills, I came up with the following:<BR>\n" );
document.write( "x=9pq-5p+2q-2. <BR>\n" );
document.write( "YOU MADE A MISTAKE HERE..JUST SEE <BR>\n" );
document.write( "x=4pq-5(1-q)-2(1-p)q+3(1-p)(1-q).<BR>\n" );
document.write( "=4PQ-5+5Q-2Q+2PQ+3-3P-3Q+3PQ<BR>\n" );
document.write( "=9PQ-3P-2....HOW DID YOU GET x=9pq-5p+2q-2. ?..CHECK....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I tried the \"collecting like terms\" operation, but I obviously veered off the right path somewhere. Could someone show me the light here, please? With many thanks, RR<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );