document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=221983>Question 221983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I am trying to figure out if I am on the right track. For some reason I just can't understand how to factor. Thanks in advance.\r<BR>\n" );
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document.write( "2t^2 y^4 - 32t^2 (I think at this point I can factor out the t^2)\r<BR>\n" );
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document.write( "t^2 (2y^4 - 32) (do I factor the parentheses at this point? I'm not sure where to go from here.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #166316 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=166316\">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=2t%5E2y%5E4-32t%5E2 ALIGN=MIDDLE  ALT=\"2t%5E2y%5E4-32t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2%28y%5E4-16%29 ALIGN=MIDDLE  ALT=\"2t%5E2%28y%5E4-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2 ALIGN=MIDDLE  ALT=\"2t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's focus on the inner expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4-16 ALIGN=MIDDLE  ALT=\"y%5E4-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4-16 ALIGN=MIDDLE  ALT=\"y%5E4-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%29%5E2-16 ALIGN=MIDDLE  ALT=\"%28y%5E2%29%5E2-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4 ALIGN=MIDDLE  ALT=\"y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%5E2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%29%5E2-%284%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%5E2%29%5E2-%284%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%5E2 ALIGN=MIDDLE  ALT=\"%284%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Notice how we have a difference of squares. So let's use the difference of squares formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2-B%5E2=%28A%2BB%29%28A-B%29 ALIGN=MIDDLE  ALT=\"A%5E2-B%5E2=%28A%2BB%29%28A-B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to factor the expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%2B4%29%28y%5E2-4%29 ALIGN=MIDDLE  ALT=\"%28y%5E2%2B4%29%28y%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the expression using the difference of squares.\r<BR>\n" );
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document.write( "You can then factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-4 ALIGN=MIDDLE  ALT=\"y%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > further (using the difference of squares rule described above) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-4=%28y%2B2%29%28y-2%29 ALIGN=MIDDLE  ALT=\"y%5E2-4=%28y%2B2%29%28y-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4-16 ALIGN=MIDDLE  ALT=\"y%5E4-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%2B4%29%28y%2B2%29%28y-2%29 ALIGN=MIDDLE  ALT=\"%28y%5E2%2B4%29%28y%2B2%29%28y-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In other words <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4-16=%28y%5E2%2B4%29%28y%2B2%29%28y-2%29 ALIGN=MIDDLE  ALT=\"y%5E4-16=%28y%5E2%2B4%29%28y%2B2%29%28y-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2%28y%5E4-16%29 ALIGN=MIDDLE  ALT=\"2t%5E2%28y%5E4-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then factors further to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2%28y%5E2%2B4%29%28y%2B2%29%28y-2%29 ALIGN=MIDDLE  ALT=\"2t%5E2%28y%5E2%2B4%29%28y%2B2%29%28y-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2y%5E4-32t%5E2 ALIGN=MIDDLE  ALT=\"2t%5E2y%5E4-32t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > completely factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2%28y%5E2%2B4%29%28y%2B2%29%28y-2%29 ALIGN=MIDDLE  ALT=\"2t%5E2%28y%5E2%2B4%29%28y%2B2%29%28y-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2y%5E4-32t%5E2=2t%5E2%28y%5E2%2B4%29%28y%2B2%29%28y-2%29 ALIGN=MIDDLE  ALT=\"2t%5E2y%5E4-32t%5E2=2t%5E2%28y%5E2%2B4%29%28y%2B2%29%28y-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "     </SPAN>\n" );
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