document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199408>Question 1199408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square poster is replaced by a rectangular poster that is 2 inches wider and 2 inches shorter. What is the difference in the number of square inches between the area of the larger poster and the smaller poster? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833276 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833276\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = side length of the original square<BR>\n" );
document.write( "This is some positive real number.\r<BR>\n" );
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document.write( "The rectangular poster is 2 inches wider.<BR>\n" );
document.write( "This means x becomes x+2 along the width.<BR>\n" );
document.write( "Meanwhile, the height goes from x to x-2 because it's 2 inches shorter.\r<BR>\n" );
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document.write( "The square poster is x inches by x inches.<BR>\n" );
document.write( "The rectangular poster is (x+2) inches by (x-2) inches.\r<BR>\n" );
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document.write( "A = area of the square = side*side = x*x = x^2<BR>\n" );
document.write( "B = area of the rectangle = width*height = (x+2)(x-2) = x^2-4<BR>\n" );
document.write( "Use the difference of squares rule to see why (x+2)(x-2) = x^2-4.\r<BR>\n" );
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document.write( "In short<BR>\n" );
document.write( "A = x^2<BR>\n" );
document.write( "B = x^2-4\r<BR>\n" );
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document.write( "Subtract these items to find that<BR>\n" );
document.write( "A - B = (x^2) - (x^2-4) = x^2-x^2+4 = 4 <BR>\n" );
document.write( "So<BR>\n" );
document.write( "A-B = 4\r<BR>\n" );
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document.write( "The difference in area is 4 square inches. \r<BR>\n" );
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document.write( "The square has the larger area because we subtracted off 4 in the area of the rectangle.\r<BR>\n" );
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document.write( "Put another way:<BR>\n" );
document.write( "A = area of the square = x^2<BR>\n" );
document.write( "B = area of the rectangle = x^2-4 = A-4\r<BR>\n" );
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document.write( "If you wanted, you could do a numeric example to help cement things better.\r<BR>\n" );
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document.write( "Let's say the square poster is 10 inches by 10 inches.<BR>\n" );
document.write( "Feel free to pick whatever positive number you prefer.<BR>\n" );
document.write( "The area is 10*10 = 100 square inches.\r<BR>\n" );
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document.write( "The rectangular poster would be 10+2 = 12 inches by 10-2 = 8 inches<BR>\n" );
document.write( "The area of this is 12*8 = 96 square inches.\r<BR>\n" );
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document.write( "Therefore, the difference in areas is 100-96 = 4 square inches.\r<BR>\n" );
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document.write( "Answer: <font color=red>4 square inches</font><BR>\n" );
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