document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4303>Question 4303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> name the quadrant in which the point (4, -70) lies </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1939 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As illustrated by Earlsdon, the problem is a difference of squares:\r<BR>\n" );
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document.write( "I thought it was strange that Earlsdon did not finish the problem by factoring the difference and sum of cubes that results from this.  Then I looked again and I noticed that your question was NOT to actually factor the problem completely.  Instead, you asked the question, \"How would I start?\"  That is exactly what he did--he got you started!!  I'm sure if he were tuned in right now, he'd be glad to finish it for you.\r<BR>\n" );
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document.write( "First, throughout my career, I have often thought about a tradition of math related to the factoring of the difference of squares.  Of course it goes like this:\r<BR>\n" );
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document.write( "Or should it be written like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+y%5E2+=+%28x%2By%29%28x-y%29 ALIGN=MIDDLE  ALT=\"x%5E2+-+y%5E2+=+%28x%2By%29%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > factor written first?\r<BR>\n" );
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document.write( "Of course both ways are completely acceptable by the commutative property, but I always tried to write it the same for my own consistency in teaching.  Moreover, I always preferred to write the (x-y) first, but I never knew why!  Finally I noticed that if you write the difference of squares formula with the (x-y) first, it makes it easier to remember the difference and sum of cubes formulas when you get to those.\r<BR>\n" );
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document.write( "Here are the three (or four) formulas:\r<BR>\n" );
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document.write( "Difference of squares:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+Prime ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+=+Prime\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (It can be factored, but not in this level of math!)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+y%5E3+=+%28x-y%29%28x%5E2%2Bxy%2By%5E2%29 ALIGN=MIDDLE  ALT=\"x%5E3+-+y%5E3+=+%28x-y%29%28x%5E2%2Bxy%2By%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+y%5E3+=+%28x%2By%29%28x%5E2-xy%2By%5E2%29 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+y%5E3+=+%28x%2By%29%28x%5E2-xy%2By%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To help remember these formulas, remember that with the <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3+-+y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > formula, you always start off with the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29 ALIGN=MIDDLE  ALT=\"%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > factor, just like I prefer to do in writing the difference of squares formula.\r<BR>\n" );
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document.write( "With the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you always start off with the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > factor.\r<BR>\n" );
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document.write( "Next notice that in BOTH formulas it is a binomial multiplied by a trinomial.  The trinomial that follows in BOTH formulas is nearly the same having a factor with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+___+xy+___+y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+___+xy+___+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The only differences in the two formulas are two signs.  The  first sign in the trinomial is always the opposite of the sign in the binomial, and the second sign in the trinomial is always positive.  Makes it easy to remember, and when you start getting older, that is really important, right? \r<BR>\n" );
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document.write( "So there you have it:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6+-+y%5E6 ALIGN=MIDDLE  ALT=\"x%5E6+-+y%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a difference of two squares.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+-+y%5E3%29%28x%5E3+%2B+y%5E3%29 ALIGN=MIDDLE  ALT=\"%28x%5E3+-+y%5E3%29%28x%5E3+%2B+y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is itself a difference and a sum of cubes.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29%28x%5E2%2Bxy%2By%5E2%29%28x%2By%29%28x%5E2-xy%2By%5E2%29 ALIGN=MIDDLE  ALT=\"%28x-y%29%28x%5E2%2Bxy%2By%5E2%29%28x%2By%29%28x%5E2-xy%2By%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "R^2 from SCC\r<BR>\n" );
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document.write( "			 </SPAN>\n" );
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