document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238426>Question 238426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^(2n+1)-2x^(n+1)+x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175179 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=175179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%282n%2B1%29-2x%5E%28n%2B1%29%2Bx ALIGN=MIDDLE  ALT=\"x%5E%282n%2B1%29-2x%5E%28n%2B1%29%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Is there something missing? Without an equals sign this is just an expression. And all you can do with an expression is simplify it or factor it.<br><BR>\n" );
document.write( "Since your expression does not simplify any farther all we can do is factor it. To see how to factor it I am going to use the property of exponents, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28%28p%2Bq%29%29+=+a%5Ep%2Aa%5Eq ALIGN=MIDDLE  ALT=\"a%5E%28%28p%2Bq%29%29+=+a%5Ep%2Aa%5Eq\"   DISABLED_style= \"max-width:90%; height:auto;\" > to rewrite the first two terms in a way that makes the common factor easier to see:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%282n%29%2Ax%5E1%29-2%28x%5En%2Ax%5E1%29%2Bx ALIGN=MIDDLE  ALT=\"x%5E%282n%29%2Ax%5E1%29-2%28x%5En%2Ax%5E1%29%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%282n%29%2Ax%29-2%28x%5En%2Ax%29%2Bx ALIGN=MIDDLE  ALT=\"x%5E%282n%29%2Ax%29-2%28x%5En%2Ax%29%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can now see that x is a common factor which we can factor out:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5E%282n%29-2x%5En+%2B+1%29 ALIGN=MIDDLE  ALT=\"x%28x%5E%282n%29-2x%5En+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And now we can factor the second factor as a perfect square trinomial. (It may be easier to see this as a perfect square trinomial if we use the property of exponents, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28%28p%2Aq%29%29+=+%28a%5Ep%29%5Eq%29 ALIGN=MIDDLE  ALT=\"a%5E%28%28p%2Aq%29%29+=+%28a%5Ep%29%5Eq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to rewrite the first term:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28%28x%5En%29%5E2-2x%5En+%2B+1%29 ALIGN=MIDDLE  ALT=\"x%28%28x%5En%29%5E2-2x%5En+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This fits the perfect square trinomial pattern, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-2ab+%2B+b%5E2+=+%28a-b%29%28a-b%29+=+%28a-b%29%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+-2ab+%2B+b%5E2+=+%28a-b%29%28a-b%29+=+%28a-b%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where \"a\" is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5En ALIGN=MIDDLE  ALT=\"x%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > and \"b\" is 1. Now we can use the pattern to factor it into:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5En+-+1%29%5E2 ALIGN=MIDDLE  ALT=\"x%28x%5En+-+1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If there was an \"= 0\" missing in the original equation, we would use factoring to solve it. We would now have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5En+-+1%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"x%28x%5En+-+1%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And this would be true only if<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5En+-+1+=+0 ALIGN=MIDDLE  ALT=\"x%5En+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Without knowing n we will not be able to find all the solutions to the second equation. But one solution is x = 1.<br><BR>\n" );
document.write( "So, if the problem was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%282n%2B1%29-2x%5E%28n%2B1%29%2Bx+=+0 ALIGN=MIDDLE  ALT=\"x%5E%282n%2B1%29-2x%5E%28n%2B1%29%2Bx+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, two solutions are:<BR>\n" );
document.write( "x = 0 or x = 1\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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