document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208443>Question 208443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me find the answer to this equation\r<BR>\n" );
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document.write( "(5x^2+7y-6z^2) (4y+3x^2) (2y-2x^2)\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157664 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the solution to this is being very careful with the piece parts as you go along.<BR>\n" );
document.write( "if you break this down, you have the equivalent of:<BR>\n" );
document.write( "(a + b + c) * (d + e) * (f + g)<BR>\n" );
document.write( "forget the minus signs for now.  they'll just muddy up the waters.<BR>\n" );
document.write( "first you need to multiply:<BR>\n" );
document.write( "(a + b + c) * (d + e)<BR>\n" );
document.write( "you will get:<BR>\n" );
document.write( "([ad + bd + cd] + [ae + be + ce])<BR>\n" );
document.write( "next you will need to multiply:<BR>\n" );
document.write( "(ad + bd + cd + ae + be + ce) * (f + g)<BR>\n" );
document.write( "you will get:<BR>\n" );
document.write( "([adf + bdf + cdf + aef + bef + cef] + [adg + bdg + cdg + aeg + beg + ceg])<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "once you finish all that you will combine all like terms and you should be done.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "nice and slow and keeping track of everything and keeping the xyz in that order will help.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let's go back to your equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2%2B7y-6z%5E2%29+%2A+%284y%2B3x%5E2%29+%2A+%282y-2x%5E2%29 ALIGN=MIDDLE  ALT=\"%285x%5E2%2B7y-6z%5E2%29+%2A+%284y%2B3x%5E2%29+%2A+%282y-2x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "first we want to multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2%2B7y-6z%5E2%29+%2A+%284y%2B3x%5E2%29 ALIGN=MIDDLE  ALT=\"%285x%5E2%2B7y-6z%5E2%29+%2A+%284y%2B3x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is broken down in two steps:<BR>\n" );
document.write( "first step is to multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2%2B7y-6z%5E2%29+%2A+%284y%29 ALIGN=MIDDLE  ALT=\"%285x%5E2%2B7y-6z%5E2%29+%2A+%284y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%5E2y ALIGN=MIDDLE  ALT=\"20x%5E2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28y%5E2 ALIGN=MIDDLE  ALT=\"28y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24yz%5E2 ALIGN=MIDDLE  ALT=\"24yz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember to keep xyz order as much as possible).<BR>\n" );
document.write( "second step is to multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2%2B7y-6z%5E2%29+%2A+%283x%5E2%29 ALIGN=MIDDLE  ALT=\"%285x%5E2%2B7y-6z%5E2%29+%2A+%283x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E4 ALIGN=MIDDLE  ALT=\"15x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21x%5E2y ALIGN=MIDDLE  ALT=\"21x%5E2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%5E2z%5E2 ALIGN=MIDDLE  ALT=\"18x%5E2z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your answer so far is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%5E2y+%2B+28y%5E2+-+24yz%5E2+%2B+15x%5E4+%2B+21x%5E2y+-+18x%5E2z%5E2 ALIGN=MIDDLE  ALT=\"20x%5E2y+%2B+28y%5E2+-+24yz%5E2+%2B+15x%5E4+%2B+21x%5E2y+-+18x%5E2z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we won't do any combining yet.<BR>\n" );
document.write( "we'll finish all the multiplications and then combine.<BR>\n" );
document.write( "i'm doing it this way to keep all the piece parts separate as much as possible so you can track what's going on easier.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "next you need to multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x%5E2y+%2B+28y%5E2+-+24yz%5E2+%2B+15x%5E4+%2B+21x%5E2y+-+18x%5E2z%5E2%29+%2A+%282y-2x%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is also broken down in 2 steps:<BR>\n" );
document.write( "first step is to multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x%5E2y+%2B+28y%5E2+-+24yz%5E2+%2B+15x%5E4+%2B+21x%5E2y+-+18x%5E2z%5E2%29+%2A+%282y%29 ALIGN=MIDDLE  ALT=\"%2820x%5E2y+%2B+28y%5E2+-+24yz%5E2+%2B+15x%5E4+%2B+21x%5E2y+-+18x%5E2z%5E2%29+%2A+%282y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you will get:<BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x%5E2y%5E2 ALIGN=MIDDLE  ALT=\"40x%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56y%5E3 ALIGN=MIDDLE  ALT=\"56y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48y%5E2z%5E2 ALIGN=MIDDLE  ALT=\"48y%5E2z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30x%5E4y ALIGN=MIDDLE  ALT=\"30x%5E4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42x%5E2y%5E2 ALIGN=MIDDLE  ALT=\"42x%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2yz%5E2 ALIGN=MIDDLE  ALT=\"36x%5E2yz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "second step is to multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x%5E2y+%2B+28y%5E2+-+24yz%5E2+%2B+15x%5E4+%2B+21x%5E2y+-+18x%5E2z%5E2%29+%2A+%28-2x%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you will get:<BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x%5E4y ALIGN=MIDDLE  ALT=\"40x%5E4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56x%5E2y%5E2 ALIGN=MIDDLE  ALT=\"56x%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48x%5E2yz%5E2 ALIGN=MIDDLE  ALT=\"48x%5E2yz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30x%5E6 ALIGN=MIDDLE  ALT=\"30x%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42x%5E4y ALIGN=MIDDLE  ALT=\"42x%5E4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E4z%5E2 ALIGN=MIDDLE  ALT=\"36x%5E4z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "putting this all together, you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x%5E2y%5E2+%2B+56y%5E3+-+48y%5E2z%5E2+%2B+30x%5E4y+%2B+42x%5E2y%5E2+-+36x%5E2yz%5E2+-+40x%5E4y+-+56x%5E2y%5E2+%2B+48x%5E2yz%5E2+-+30x%5E6+-+42x%5E4y+%2B+36x%5E4z%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "combining like terms, we get:<BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x%5E2y%5E2 ALIGN=MIDDLE  ALT=\"40x%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42x%5E2y%5E2 ALIGN=MIDDLE  ALT=\"42x%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56x%5E2y%5E2 ALIGN=MIDDLE  ALT=\"56x%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56y%5E3 ALIGN=MIDDLE  ALT=\"56y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48y%5E2z%5E2 ALIGN=MIDDLE  ALT=\"48y%5E2z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30x%5E4y ALIGN=MIDDLE  ALT=\"30x%5E4y\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x%5E4y ALIGN=MIDDLE  ALT=\"40x%5E4y\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42x%5E4y ALIGN=MIDDLE  ALT=\"42x%5E4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2yz%5E2 ALIGN=MIDDLE  ALT=\"36x%5E2yz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48x%5E2yz%5E2 ALIGN=MIDDLE  ALT=\"48x%5E2yz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30x%5E6 ALIGN=MIDDLE  ALT=\"30x%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E4z%5E2 ALIGN=MIDDLE  ALT=\"36x%5E4z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26x%5E2y%5E2+%2B+56y%5E3+-+48y%5E2z%5E2+-+52x%5E4y+%2B+12x%5E2yz%5E2+-+30x%5E6+%2B+36x%5E4z%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );