document.write( "Question 1209234: Fill in the blank with a constant, so that the resulting expression can be
\n" ); document.write( "factored as the product of two linear expressions:\r
\n" ); document.write( "\n" ); document.write( "2ab - a + b + ___ \n" ); document.write( "
Algebra.Com's Answer #847886 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "I hope you understand FOIL, i.e., FIRSTS, OUTERS, INNERS, LASTS. I'm assuming you do.\r\n" );
document.write( "\r\n" );
document.write( "2ab - a + b + ___\r\n" );
document.write( "\r\n" );
document.write( "Write this:\r\n" );
document.write( "\r\n" );
document.write( "(__ ± __)(__ ± __)\r\n" );
document.write( "\r\n" );
document.write( "Let's fix up the FIRSTS to be 2ab.  We will split 2ab up into factors 2a and b\r\n" );
document.write( "and put them for the FIRSTS\r\n" );
document.write( "\r\n" );
document.write( "(2a ± __)(b ± __)\r\n" );
document.write( "\r\n" );
document.write( "Now let's fix up the OUTERS.  We notice to get the term \" -a \" for the OUTERS,\r\n" );
document.write( "we will need the term on the far right to be -1/2.\r\n" );
document.write( "\r\n" );
document.write( "(2a ± __)(b - 1/2)\r\n" );
document.write( "\r\n" );
document.write( "Now let's fix up the INNERS.  We notice to get the term +b for the\r\n" );
document.write( "INNERS, we will need the term +1 in the remaining blank:\r\n" );
document.write( "\r\n" );
document.write( "(2a + 1)(b - 1/2)  <--factorization as the product of two linear expressions\r\n" );
document.write( "\r\n" );
document.write( "The LASTS are now already fixed up. \r\n" );
document.write( "\r\n" );
document.write( "So we proceed to FOIL that out:\r\n" );
document.write( "\r\n" );
document.write( "(2a)(b)+(2a)(-1/2)+(+1)(b)+(1)(-1/2)\r\n" );
document.write( "\r\n" );
document.write( "2ab - a + b + (-1/2)\r\n" );
document.write( "\r\n" );
document.write( "So we see that the answer is -1/2\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );