document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924361>Question 924361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm doing a problem online and it says that:<BR>\n" );
document.write( "a * a^&#8203;3 + 3a^&#8203;2&#8203;&#8203;b + 3ab^&#8203;2&#8203; + b^&#8203;3 = a&#8203;^4 + 3a&#8203;^3&#8203;&#8203;b + 3a&#8203;^2&#8203;&#8203;b&#8203;^2&#8203; + ab^&#8203;3 &#8203;+ 0b^&#8203;4&#8203;&#8203;. I have no idea where the 0b^4 is coming from. Can anyone explain this? Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560785 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=560785\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it has to be a computer glitch.<BR>\n" );
document.write( "there's no mathematical reason for it to be there.\r<BR>\n" );
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document.write( "the only reason i can think for it to be there would be that (a+b)^4 ends in b^4 when you are dealing with the binomial expansion theorem.\r<BR>\n" );
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document.write( "in fact, your original equation is the binomial expansion of (a+b)^3.\r<BR>\n" );
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document.write( "that leads me to believe that this is something like an aberrated application of (a+b)^4 where the computer doesn't know to remove 0b^4.\r<BR>\n" );
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document.write( "consider:\r<BR>\n" );
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document.write( "(a+b) * a = a^2 + ab\r<BR>\n" );
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document.write( "now consider:\r<BR>\n" );
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document.write( "(a+b) * (a + 0b)\r<BR>\n" );
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document.write( "you could get 0b * b = 0b^2 at the end.\r<BR>\n" );
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document.write( "in the middle it handles it ok but in the end it sticks out because the algorithm didn't know how to finish the job completely.\r<BR>\n" );
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document.write( "(a+b) * (a + 0b) is equal to a*a + a*0b + b*a + 0b*b\r<BR>\n" );
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document.write( "this can be simplified to:\r<BR>\n" );
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document.write( "a^2 + 0*a*b + a*b + 0*b*b\r<BR>\n" );
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document.write( "simplify this further and you get:\r<BR>\n" );
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document.write( "a^2 + a*b + 0*b^2\r<BR>\n" );
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document.write( "the computer was able to handle 0*a*b + a*b which resulted in a*b.\r<BR>\n" );
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document.write( "the computer didn't think it had to do anything else with 0*b*b so it left it as 0*b^2.\r<BR>\n" );
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document.write( "bottom line is it doesn't really belong there.\r<BR>\n" );
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document.write( "i'm not sure what you were supposed to do with that problem, but i would guess if you got the answer wrong because of that situation, then you have an argument to change that decision.\r<BR>\n" );
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document.write( "it's not technically wrong because 0*b^4 is equal to 0, but it doesn't really belong there.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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