document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=829497>Question 829497</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use algebra to explain why the middle term 2ab is needed in the expression (a + b)² = a² + 2ab + b².<BR>\n" );
document.write( "Use geometry to explain why the term 2ab is needed. Specifically, notice that the area of a square with side a + b is (a + b)². On the other hand, this area is the sum of areas of both squares, plus the areas of the two rectangles <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 #499882 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=499882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Exactly as you described.  You can represent a square composed of sides, a+b.  The lengths a and b can each be projected at right angles from each of this square's sides.  In this projective action, a and b from each side will sweep into these four areas:\r<BR>\n" );
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document.write( "a*a, b*b, and TWO of a*b.\r<BR>\n" );
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document.write( "The a*b may be a rectangle.  The a*a and b*b are both squares.  \r<BR>\n" );
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document.write( "All that is very easy to draw and label.  Seeing and understanding is also easier that way.\r<BR>\n" );
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document.write( "If you will do all that, you will also see why the Distributive Property of \"Algebra 1, 2, and 3\" work. </SPAN>\n" );
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