document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205236>Question 1205236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the constant term in the binomial expansion of (4𝑥^3 − 1/2𝑥^2)^15. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841910 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841910\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The problem is posted incorrectly.<br><BR>\n" );
document.write( "The sequence of characters \"1/2x^2\" is ambiguous.<br><BR>\n" );
document.write( "If that means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x%5E2 ALIGN=MIDDLE  ALT=\"%281%2F2%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then there is of course no constant term in the expansion.<br><BR>\n" );
document.write( "But if it means (as it surely was intended to!) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282x%5E2%29 ALIGN=MIDDLE  ALT=\"1%2F%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then there is a constant term.<br><BR>\n" );
document.write( "Any student who is working on a problem like this should have enough experience with mathematics to know that proper use of parentheses is important.<br><BR>\n" );
document.write( "Assuming the latter meaning, the constant term will occur when the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3%29 ALIGN=MIDDLE  ALT=\"4x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is to the 6th power and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282x%5E2%29 ALIGN=MIDDLE  ALT=\"1%2F%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is to the 9th power.  That constant term is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%2815%2C6%29%29%284%5E6%29%28%28-1%2F2%29%5E9%29=%285005%29%282%5E12%29%28-2%5E%28-9%29%29=5005%28-2%5E3%29=5005%28-8%29=-40040 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: -40040<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );