document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74016>Question 74016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (4x+y)(2x squared-xy+5y squared) find the product </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53030 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=53030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%2By%29%2A%282x%5E2-xy+%2B5y%5E2%29 ALIGN=MIDDLE  ALT=\"%284x%2By%29%2A%282x%5E2-xy+%2B5y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Here's the general plan to find the product. Use each term in the first set of parentheses<BR>\n" );
document.write( "one at a time and multiply it times each of the three terms in the second set of parentheses.<BR>\n" );
document.write( "Then add all the resulting terms from both multiplications. Finally look for common terms<BR>\n" );
document.write( "and combine them.<BR>\n" );
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document.write( "Following that plan, let's multiply 4x times every term in the second set of parentheses.<BR>\n" );
document.write( "(Remember that you will add exponents if the term from the second set of parentheses<BR>\n" );
document.write( "already has an x in it.)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2A+%282x%5E2-xy+%2B5y%5E2%29+=+%284x%2A2x%5E2%29+-%284x%2Axy%29+%2B+%284x%2A5y%5E2%29+=+8x%5E3+-4x%5E2y+%2B+20xy%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next multiply the three terms in the second set of parentheses by the +y from the first<BR>\n" );
document.write( "set of parentheses to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2A%282x%5E2-xy+%2B5y%5E2%29+=+%28y%2A2x%5E2%29-+%28x%2Ay%5E2%29+%2B+%28y%2A5y%5E2%29+=+2x%5E2y+-+xy%5E2+%2B5y%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the results of the two multiplications together to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3+-4x%5E2y+%2B+20xy%5E2+%2B+2x%5E2y+-+xy%5E2+%2B5y%5E3 ALIGN=MIDDLE  ALT=\"8x%5E3+-4x%5E2y+%2B+20xy%5E2+%2B+2x%5E2y+-+xy%5E2+%2B5y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now look for common terms that can be combined:<BR>\n" );
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document.write( "How about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2y+ ALIGN=MIDDLE  ALT=\"-4x%5E2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2y ALIGN=MIDDLE  ALT=\"2x%5E2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. These add together to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2y ALIGN=MIDDLE  ALT=\"-2x%5E2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. When you <BR>\n" );
document.write( "replace these two terms with the single resulting term the answer reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3+-2x%5E2y+%2B+20xy%5E2+-+xy%5E2+%2B5y%5E3 ALIGN=MIDDLE  ALT=\"8x%5E3+-2x%5E2y+%2B+20xy%5E2+-+xy%5E2+%2B5y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next, notice the two terms that contain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%5E2 ALIGN=MIDDLE  ALT=\"xy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Combining these results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20xy%5E2+-+xy%5E2+=+19xy%5E2 ALIGN=MIDDLE  ALT=\"20xy%5E2+-+xy%5E2+=+19xy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and substituting this into the answer gives:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3+-2x%5E2y+%2B+19xy%5E2+%2B5y%5E3 ALIGN=MIDDLE  ALT=\"8x%5E3+-2x%5E2y+%2B+19xy%5E2+%2B5y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's it. There are no more common terms so this is the answer to your multiplication<BR>\n" );
document.write( "problem.<BR>\n" );
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document.write( "Hope that you can track this.   </SPAN>\n" );
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