document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73547>Question 73547</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495188891/algebrahomeworkh>Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely: x^7y^2 - 4x^5y^2 - 21x^3y^2\r<BR>\n" );
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document.write( "I am having a difficult time factoring this trinominal. Think I am getting confused by all the x's and y's.  Could you please help me, so I can work these types of problems correctly?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52614 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=52614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factor:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E7y%5E2+-+4x%5E5y%5E2+-+21x%5E3y%5E2 ALIGN=MIDDLE  ALT=\"+x%5E7y%5E2+-+4x%5E5y%5E2+-+21x%5E3y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "First look to see if there are any common factors in every term.  Note that every term has<BR>\n" );
document.write( "a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in it. So pull that out and make it a multiplier of all the terms.  You should<BR>\n" );
document.write( "find that you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2A%28x%5E7+-+4x%5E5+-+21x%5E3%29 ALIGN=MIDDLE  ALT=\"y%5E2%2A%28x%5E7+-+4x%5E5+-+21x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Look at what is left in the parentheses. All of the terms contain an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > so factor it<BR>\n" );
document.write( "out and make it another multiplier of the expression remaining in the parentheses.  When you<BR>\n" );
document.write( "do the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Ax%5E3%2A%28x%5E4+-+4x%5E2+-+21%29 ALIGN=MIDDLE  ALT=\"y%5E2%2Ax%5E3%2A%28x%5E4+-+4x%5E2+-+21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So far, so good.  Now examine what's left in the parentheses.  You may not recognize<BR>\n" );
document.write( "it, but it can be factored like a quadratic.  It may help you to see that if you let <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+x%5E2 ALIGN=MIDDLE  ALT=\"A+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then the expression in the parentheses would become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2+-+4A+-+21 ALIGN=MIDDLE  ALT=\"A%5E2+-+4A+-+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you may not be able to see that this factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A+-+7%29%2A%28A%2B3%29 ALIGN=MIDDLE  ALT=\"%28A+-+7%29%2A%28A%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you can plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+ ALIGN=MIDDLE  ALT=\"x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > back in for A to get the two factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-+4x%5E2+-21 ALIGN=MIDDLE  ALT=\"x%5E4+-+4x%5E2+-21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "as being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-7%29%2A%28x%5E2+%2B+3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-7%29%2A%28x%5E2+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So this is where we are at this point:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Ax%5E3%2A%28x%5E2+-+7%29%2A%28x%5E2+%2B+3%29 ALIGN=MIDDLE  ALT=\"y%5E2%2Ax%5E3%2A%28x%5E2+-+7%29%2A%28x%5E2+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This may be good enough for the answer you are to provide, but there is one more mathematical <BR>\n" );
document.write( "trick you can use on this.  The term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+7 ALIGN=MIDDLE  ALT=\"x%5E2+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the difference of two squares.<BR>\n" );
document.write( "Therefore its factors are the sum and difference of the square roots of each term in <BR>\n" );
document.write( "the parentheses.  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+7 ALIGN=MIDDLE  ALT=\"x%5E2+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+sqrt%287%29%29%2A%28x+%2B+sqrt%287%29%29 ALIGN=MIDDLE  ALT=\"%28x+-+sqrt%287%29%29%2A%28x+%2B+sqrt%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This final<BR>\n" );
document.write( "step completes what can be done by factoring.  The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Ax%5E3%2A%28x-sqrt%287%29%29%2A%28x%2Bsqrt%287%29%29%2A%28x%5E2+%2B+3%29 ALIGN=MIDDLE  ALT=\"y%5E2%2Ax%5E3%2A%28x-sqrt%287%29%29%2A%28x%2Bsqrt%287%29%29%2A%28x%5E2+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This last step all depends on whether your teacher expects you to be working with radicals<BR>\n" );
document.write( "in the answer.<BR>\n" );
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document.write( "Hope this helps. </SPAN>\n" );
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