document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257890>Question 257890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Apply the order of operations to simplify the following expression. 2x[(5x^2-3x+2)-(6x^3+6x^2)/3x^2] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189789 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=189789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> expression is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2A%28%285%2Ax%5E2-3%2Ax%2B2%29-%286%2Ax%5E3%2B6%2Ax%5E2%29%2F%283%2Ax%5E2%29%29 ALIGN=MIDDLE  ALT=\"2%2Ax%2A%28%285%2Ax%5E2-3%2Ax%2B2%29-%286%2Ax%5E3%2B6%2Ax%5E2%29%2F%283%2Ax%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you process operations within parentheses first starting from the inner parentheses and working to the outer parentheses.\r<BR>\n" );
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document.write( "your expressions within the inner parentheses can't be processed any further.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Ax%5E2-3%2Ax%2B2%29 ALIGN=MIDDLE  ALT=\"%285%2Ax%5E2-3%2Ax%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Ax%5E3%2B6%2Ax%5E2%29 ALIGN=MIDDLE  ALT=\"%286%2Ax%5E3%2B6%2Ax%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Ax%5E2%29 ALIGN=MIDDLE  ALT=\"%283%2Ax%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your terms in the outer parentheses need to be processed next.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285%2Ax%5E2-3%2Ax%2B2%29-%286%2Ax%5E3%2B6%2Ax%5E2%29%2F%283%2Ax%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28%285%2Ax%5E2-3%2Ax%2B2%29-%286%2Ax%5E3%2B6%2Ax%5E2%29%2F%283%2Ax%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you would need to divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Ax%5E3%2B6%2Ax%5E2%29 ALIGN=MIDDLE  ALT=\"%286%2Ax%5E3%2B6%2Ax%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Ax%5E2%29 ALIGN=MIDDLE  ALT=\"%283%2Ax%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > first.\r<BR>\n" );
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document.write( "that gets you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ax+%2B+2%29 ALIGN=MIDDLE  ALT=\"%282%2Ax+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the expression within the outer parenthese becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285%2Ax%5E2-3%2Ax%2B2%29+-+%282%2Ax+%2B+2%29%29 ALIGN=MIDDLE  ALT=\"%28%285%2Ax%5E2-3%2Ax%2B2%29+-+%282%2Ax+%2B+2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you process this next by removing the inner parentheses from the outer parentheses to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Ax%5E2+-+3%2Ax+%2B+2+-+2%2Ax+-+2%29%29 ALIGN=MIDDLE  ALT=\"%285%2Ax%5E2+-+3%2Ax+%2B+2+-+2%2Ax+-+2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Ax%5E2+-+5%2Ax%29 ALIGN=MIDDLE  ALT=\"%285%2Ax%5E2+-+5%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you replace the original expression within the outer parentheses by this to make your original equation of:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2A%28%285%2Ax%5E2-3%2Ax%2B2%29-%286%2Ax%5E3%2B6%2Ax%5E2%29%2F%283%2Ax%5E2%29%29 ALIGN=MIDDLE  ALT=\"2%2Ax%2A%28%285%2Ax%5E2-3%2Ax%2B2%29-%286%2Ax%5E3%2B6%2Ax%5E2%29%2F%283%2Ax%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2A%285%2Ax%5E2+-+5%2Ax%29 ALIGN=MIDDLE  ALT=\"2%2Ax%2A%285%2Ax%5E2+-+5%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you multiply each term within the parentheses by 2*x to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax%5E3+-+10%2Ax%5E2 ALIGN=MIDDLE  ALT=\"10%2Ax%5E3+-+10%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if you did this right, then you should be able to get the same results in the original equation and the final equation for any value of x.\r<BR>\n" );
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document.write( "take x = 5\r<BR>\n" );
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document.write( "final equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax%5E3+-+10%2Ax%5E2 ALIGN=MIDDLE  ALT=\"10%2Ax%5E3+-+10%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A5%5E3+-+10%2A5%5E2+=+1000 ALIGN=MIDDLE  ALT=\"10%2A5%5E3+-+10%2A5%5E2+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "original equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%2A%28%285%2Ax%5E2-3%2Ax%2B2%29-%286%2Ax%5E3%2B6%2Ax%5E2%29%2F%283%2Ax%5E2%29%29 ALIGN=MIDDLE  ALT=\"2%2Ax%2A%28%285%2Ax%5E2-3%2Ax%2B2%29-%286%2Ax%5E3%2B6%2Ax%5E2%29%2F%283%2Ax%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A5%2A%28%285%2A5%5E2+-+3%2A5+%2B+2%29+-+%286%2A5%5E3+%2B+6%2A5%5E2%29%2F%283%2A5%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2A+%28%28125+-+15+%2B+2%29+-+%28750+%2B+150%29%2F75%29 ALIGN=MIDDLE  ALT=\"10+%2A+%28%28125+-+15+%2B+2%29+-+%28750+%2B+150%29%2F75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2A+%28%28112%29+-+%28900%2F75%29%29 ALIGN=MIDDLE  ALT=\"10+%2A+%28%28112%29+-+%28900%2F75%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2A+100 ALIGN=MIDDLE  ALT=\"10+%2A+100\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "1000\r<BR>\n" );
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document.write( "since they both come up with the same answer, the final equation is equivalent to the original equation which indicates we simplified the equation properly.\r<BR>\n" );
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document.write( "the simplified equation is:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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