document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27810>Question 27810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would really appreciate any help you could can give me regarding the two following problems.  The instructions are to Factor the polynomial.  I have been able to do the others, but for some reason these two have me stuck.\r<BR>\n" );
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document.write( "Factor Completely<BR>\n" );
document.write( "Problem One - 64-(r+2t)^2<BR>\n" );
document.write( "Problem Two - -k^2-h^2+2kh+4\r<BR>\n" );
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document.write( "Thanks in advance for your assistance<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15146 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=15146\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) Factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64-%28r%2B2t%29%5E2 ALIGN=MIDDLE  ALT=\"64-%28r%2B2t%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > You should recognise this as the difference of two squares: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+=+8%5E2 ALIGN=MIDDLE  ALT=\"64+=+8%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B2t%29%5E2 ALIGN=MIDDLE  ALT=\"%28r%2B2t%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " The difference of two squares can be factored:<BR>\n" );
document.write( "<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;\" > Appplying this to your problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2+-+%28r%2B2t%29%5E2+=+%288+%2B+%28r%2B2t%29%29%288+-+%28r%2B2t%29%29 ALIGN=MIDDLE  ALT=\"8%5E2+-+%28r%2B2t%29%5E2+=+%288+%2B+%28r%2B2t%29%29%288+-+%28r%2B2t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2Br%2B2t%29%288-r-2t%29 ALIGN=MIDDLE  ALT=\"%288%2Br%2B2t%29%288-r-2t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2) Factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-k%5E2-h%5E2%2B2kh%2B4 ALIGN=MIDDLE  ALT=\"-k%5E2-h%5E2%2B2kh%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > If you rearrange this expression, you will see that it is really the difference of two squares.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+-+%28k%5E2-2kh%2Bh%5E2%29 ALIGN=MIDDLE  ALT=\"4+-+%28k%5E2-2kh%2Bh%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the parentheses.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+-+%28k-h%29%5E2 ALIGN=MIDDLE  ALT=\"4+-+%28k-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now it's in the form of: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2+-+b%5E2 ALIGN=MIDDLE  ALT=\"A%5E2+-+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >which will factor nicely.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+-+%28k-h%29%5E2+=+%282+%2B+%28k-h%29%29%282+-+%28k-h%29%29 ALIGN=MIDDLE  ALT=\"4+-+%28k-h%29%5E2+=+%282+%2B+%28k-h%29%29%282+-+%28k-h%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Bk-h%29%282-k%2Bh%29 ALIGN=MIDDLE  ALT=\"%282%2Bk-h%29%282-k%2Bh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can verify these answers by multiplying the factors to see that you get back the original expressions.<BR>\n" );
document.write( "I'll leave this as an exercise for the student! </SPAN>\n" );
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