document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=111596>Question 111596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please explain.\r<BR>\n" );
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document.write( "b^2-2bc+c^2=(b-c)^2\r<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 #81384 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=81384\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> => these are the square of binomials: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-b%29%5E2 ALIGN=MIDDLE  ALT=\"%28a-b%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Important to know: \r<BR>\n" );
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document.write( "If the binomial has a minus sign, then the minus sign appears <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=only ALIGN=MIDDLE  ALT=\"only\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%0D%0A%0D%0Ain ALIGN=MIDDLE  ALT=\"+%0D%0A%0D%0Ain\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+the ALIGN=MIDDLE  ALT=\"+the\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+middle ALIGN=MIDDLE  ALT=\"+middle\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+term ALIGN=MIDDLE  ALT=\"+term\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the trinomial.  \r<BR>\n" );
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document.write( "If the binomial is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b ALIGN=MIDDLE  ALT=\"a+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the middle term will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B2ab ALIGN=MIDDLE  ALT=\"%2B2ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  \r<BR>\n" );
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document.write( "and if the binomial is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+-+b ALIGN=MIDDLE  ALT=\"a+-+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the middle term will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2ab ALIGN=MIDDLE  ALT=\"-2ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >; \r<BR>\n" );
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document.write( "therefore, we can use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=double+ ALIGN=MIDDLE  ALT=\"double+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sign ALIGN=MIDDLE  ALT=\"sign\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (\"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=plus_+or_+minus ALIGN=MIDDLE  ALT=\"plus_+or_+minus\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"), \r<BR>\n" );
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document.write( "to state the rule as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+%2B-+b%29%5E2+=+a%5E2+%2B-+2ab+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"%28a+%2B-+b%29%5E2+=+a%5E2+%2B-+2ab+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The square of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=any+ ALIGN=MIDDLE  ALT=\"any+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=binomial ALIGN=MIDDLE  ALT=\"binomial\"   DISABLED_style= \"max-width:90%; height:auto;\" > produces the following three terms:\r<BR>\n" );
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document.write( "1.   The square of the first term of the binomial: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E2 ALIGN=MIDDLE  ALT=\"+a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.   Twice the product of the two terms:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B-2ab ALIGN=MIDDLE  ALT=\"%2B-2ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3.   The square of the second term:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The square of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=every ALIGN=MIDDLE  ALT=\"every\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+binomial ALIGN=MIDDLE  ALT=\"+binomial\"   DISABLED_style= \"max-width:90%; height:auto;\" >, called a perfect square trinomial, \r<BR>\n" );
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document.write( "has that form:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B-+2ab+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B-+2ab+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "So, if your square your binomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-c%29%5E2 ALIGN=MIDDLE  ALT=\"%28b-c%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it will be:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28b-c%29%5E2+=+b%5E2+-2bc+%2B+c%5E2 ALIGN=MIDDLE  ALT=\"+%28b-c%29%5E2+=+b%5E2+-2bc+%2B+c%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=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the square of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   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=-2bc+ ALIGN=MIDDLE  ALT=\"-2bc+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is  twice the product of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%2A%28-c%29+=+-2bc++ ALIGN=MIDDLE  ALT=\"2b%2A%28-c%29+=+-2bc++\"   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=c%5E2 ALIGN=MIDDLE  ALT=\"c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the square of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-c ALIGN=MIDDLE  ALT=\"-c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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