document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141476>Question 1141476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this\r<BR>\n" );
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document.write( "Use the Binomial Theorem to expand (x-3y)^5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762024 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=762024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The binomial theorem looks scary to most students when they first see it.  But with a little experience it is fairly easy to use -- especially if you understand WHY it works.<br><BR>\n" );
document.write( "So let me start you on this with a demonstration; then you can finish.<br><BR>\n" );
document.write( "The expression means you have five identical factors of (x-3y).  When you expand the expression, you are going to get terms of x^5, x^4y, x^3y^2, x^2y^3, xy^4, and y^5.<br><BR>\n" );
document.write( "Think about how many ways you are going to get each of those kinds of terms.<br><BR>\n" );
document.write( "(1) x^5...<br><BR>\n" );
document.write( "To get an x^5 term, you clearly need to choose the \"x\" term from all 5 factors (and the \"-3y\" term in 0 of them).  The number of ways you can choose the \"x\" term in all 5 of the 5 factors is \"5 choose 5\" = C(5,5) = 1.<br><BR>\n" );
document.write( "So the x^5 term will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C5%29%28%28x%29%5E5%29%28%28-3y%29%5E0%29+=+%281%29%28x%5E5%29%281%29+=+x%5E5 ALIGN=MIDDLE  ALT=\"C%285%2C5%29%28%28x%29%5E5%29%28%28-3y%29%5E0%29+=+%281%29%28x%5E5%29%281%29+=+x%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "(2) x^4y...<br><BR>\n" );
document.write( "To get an x^4y term, you need to choose the \"x\" term from 4 of the 5 factors and the \"-3y\" term in 1 of them.  The number of ways you can choose the x term in 4 of the 5 factors is \"5 choose 4\" = C(5,4) = 5.<br><BR>\n" );
document.write( "So the x^4y term will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C4%29%28%28x%29%5E4%29%28%28-3y%29%5E1%29+=+%285%29%28x%5E4%29%28-3y%29+=+-15x%5E4y ALIGN=MIDDLE  ALT=\"C%285%2C4%29%28%28x%29%5E4%29%28%28-3y%29%5E1%29+=+%285%29%28x%5E4%29%28-3y%29+=+-15x%5E4y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "(3) x^3y^2...<br><BR>\n" );
document.write( "To get an x^3y^2 term, you need to choose the \"x\" term from 3 of the 5 factors and the \"-3y\" term in 2 of them.  The number of ways you can choose the x term in 3 of the 5 factors is \"5 choose 3\" = C(5,3) = 10.<br><BR>\n" );
document.write( "So the x^3y^2 term will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C3%29%28%28x%29%5E3%29%28%28-3y%29%5E2%29+=+%2810%29%28x%5E3%29%289y%5E2%29+=+90x%5E3y%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "I'll let you fill in the calculations to finish the expansion.  The remaining terms are<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C2%29%28%28x%29%5E2%29%28%28-3y%29%5E3%29 ALIGN=MIDDLE  ALT=\"C%285%2C2%29%28%28x%29%5E2%29%28%28-3y%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C1%29%28%28x%29%5E1%29%28%28-3y%29%5E4%29 ALIGN=MIDDLE  ALT=\"C%285%2C1%29%28%28x%29%5E1%29%28%28-3y%29%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C0%29%28%28x%29%5E0%29%28%28-3y%29%5E5%29 ALIGN=MIDDLE  ALT=\"C%285%2C0%29%28%28x%29%5E0%29%28%28-3y%29%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );