document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76418>Question 76418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor:\r<BR>\n" );
document.write( "\n" );
document.write( "(w-5)(w+7)+(w-5)(w+9) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54815 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-5%29%2A%28w%2B7%29%2B%28w-5%29%2A%28w%2B9%29 ALIGN=MIDDLE  ALT=\"%28w-5%29%2A%28w%2B7%29%2B%28w-5%29%2A%28w%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Factor this expression.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that the two term (separated by the + sign tucked in between the \")\" and \"(\" symbols) <BR>\n" );
document.write( "both contain (w-5) as a factor.  Therefore this factor of (w-5) can be pulled out as an<BR>\n" );
document.write( "overall factor and the result is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-5%29%2A%28%28w%2B7%29%2B%28w%2B9%29%29 ALIGN=MIDDLE  ALT=\"%28w-5%29%2A%28%28w%2B7%29%2B%28w%2B9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the \"(w+7)\" and \"(w+9)\" quantities are both positive quantities, their parentheses<BR>\n" );
document.write( "can be removed without changing the terms they contain.  Removing these parentheses <BR>\n" );
document.write( "results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-5%29%2A%28w%2B7%2Bw%2B9%29 ALIGN=MIDDLE  ALT=\"%28w-5%29%2A%28w%2B7%2Bw%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that the quantity on the right within the parentheses can be simplified by adding<BR>\n" );
document.write( "the like terms to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-5%29%2A%282w%2B16%29 ALIGN=MIDDLE  ALT=\"%28w-5%29%2A%282w%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then notice that the terms in this simplified quantity have a common factor of 2. So<BR>\n" );
document.write( "you can pull this factor out and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-5%29%2A2%2A%28w%2B8%29 ALIGN=MIDDLE  ALT=\"%28w-5%29%2A2%2A%28w%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and this can be re-arranged into a more conventional order:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28w-5%29%28w%2B8%29 ALIGN=MIDDLE  ALT=\"2%28w-5%29%28w%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This is the answer you are looking for.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope the logical progression from one step to the next one was understandable and that<BR>\n" );
document.write( "it provides you with some added insight into the factoring and simplification processes. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );