document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63648>Question 63648</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi, i just took the practice SAT on collegeboard.com, and one problem really stumped me. here it is:\r<BR>\n" );
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document.write( "(2x)^(3y) - (2x)^y\r<BR>\n" );
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document.write( "the answer that was given was:\r<BR>\n" );
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document.write( "(2x)^y [{(2x)^(2y)}-1]\r<BR>\n" );
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document.write( "i may or may not have typed the answer incorrectly, i don't know how to. :P<BR>\n" );
document.write( "what i thought was the answer was: (2x)^2y\r<BR>\n" );
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document.write( "why not? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44366 by </B><A HREF=/tutors/aboutme.mpl?userid=joyofmath><B>joyofmath(189)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=joyofmath><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=44366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <b><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E%283y%29+-+%282x%29%5Ey ALIGN=MIDDLE  ALT=\"%282x%29%5E%283y%29+-+%282x%29%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" ></b>\r<BR>\n" );
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document.write( "The answer isn't <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E%282y%29 ALIGN=MIDDLE  ALT=\"%282x%29%5E%282y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Eb+-+a%5Ec ALIGN=MIDDLE  ALT=\"a%5Eb+-+a%5Ec\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28b-c%29 ALIGN=MIDDLE  ALT=\"a%5E%28b-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let a=3, b=2, and c=1 to show a counter-example.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Eb-a%5Ec+=+3%5E2-3%5E1+=+9-3+=+6 ALIGN=MIDDLE  ALT=\"a%5Eb-a%5Ec+=+3%5E2-3%5E1+=+9-3+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28b-c%29+=+3%5E%282-1%29+=+3%5E1+=+3 ALIGN=MIDDLE  ALT=\"a%5E%28b-c%29+=+3%5E%282-1%29+=+3%5E1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, the two expressions are not the same.\r<BR>\n" );
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document.write( "To solve the problem you first notice that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+2y%2By ALIGN=MIDDLE  ALT=\"3y+=+2y%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "What is useful here is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28b%2Bc%29+=+%28a%5Eb%29%28a%5Ec%29 ALIGN=MIDDLE  ALT=\"a%5E%28b%2Bc%29+=+%28a%5Eb%29%28a%5Ec%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E%283y%29+-+%282x%29%5Ey+=+%28%282x%29%5Ey%29%28%282x%29%5E%282y%29%29+-+%282x%29%5Ey ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You can pull out a factor of (2x)^y from the equation. You then get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%282x%29%5Ey%29%28%282x%29%5E%282y%29+-+1%29%29 ALIGN=MIDDLE  ALT=\"+%28%282x%29%5Ey%29%28%282x%29%5E%282y%29+-+1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the answer the sample test gave. </SPAN>\n" );
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