document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178268>Question 178268</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry Structure and Method book 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!\r<BR>\n" );
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document.write( "Binomials Containing Radicals<BR>\n" );
document.write( "Simplify. Assume that each radical represents a real number.<BR>\n" );
document.write( "(&#8730;(n+1) +&#8730;n)( &#8730;(n+1) -&#8730;n) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133226 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=133226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When trying to simplify or expand complicated expressions involving roots, you can try substitutions to get the expression into a cleaner form (it's not required, but I find that it helps you see the big picture).\r<BR>\n" );
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document.write( "So if we let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28n%2B1%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28n%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%28x-y%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: I just replaced every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with \"x\" and every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%29 ALIGN=MIDDLE  ALT=\"sqrt%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with \"y\")\r<BR>\n" );
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document.write( "Now let's FOIL <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%28x-y%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember, when you FOIL an expression, you follow this procedure:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28x%29%2By%29%28highlight%28x%29-y%29 ALIGN=MIDDLE  ALT=\"%28highlight%28x%29%2By%29%28highlight%28x%29-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">F</font>irst terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2A%28x%29=x%5E2 ALIGN=MIDDLE  ALT=\"%28x%29%2A%28x%29=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28x%29%2By%29%28x%2Bhighlight%28-y%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%28x%29%2By%29%28x%2Bhighlight%28-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">O</font>uter terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2A%28-y%29=-x%2Ay ALIGN=MIDDLE  ALT=\"%28x%29%2A%28-y%29=-x%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bhighlight%28y%29%29%28highlight%28x%29-y%29 ALIGN=MIDDLE  ALT=\"%28x%2Bhighlight%28y%29%29%28highlight%28x%29-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">I</font>nner terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%29%2A%28x%29=x%2Ay ALIGN=MIDDLE  ALT=\"%28y%29%2A%28x%29=x%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bhighlight%28y%29%29%28x%2Bhighlight%28-y%29%29 ALIGN=MIDDLE  ALT=\"%28x%2Bhighlight%28y%29%29%28x%2Bhighlight%28-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">L</font>ast terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%29%2A%28-y%29=-y%5E2 ALIGN=MIDDLE  ALT=\"%28y%29%2A%28-y%29=-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%2Ay%2Bx%2Ay-y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-x%2Ay%2Bx%2Ay-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now collect every term to make a single expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%28x-y%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOILs to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%28x-y%29=x%5E2-y%5E2 ALIGN=MIDDLE  ALT=\"%28x%2By%29%28x-y%29=x%5E2-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%28x-y%29=x%5E2-y%5E2 ALIGN=MIDDLE  ALT=\"%28x%2By%29%28x-y%29=x%5E2-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the last equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28sqrt%28n%2B1%29%29%2By%29%28highlight%28sqrt%28n%2B1%29%29-y%29=%28highlight%28sqrt%28n%2B1%29%29%29%5E2-y%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28n%2B1%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie replace every \"x\" with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28n%2B1%29%2Bhighlight%28sqrt%28n%29%29%29%28sqrt%28n%2B1%29-highlight%28sqrt%28n%29%29%29=%28sqrt%28n%2B1%29%29%5E2-%28highlight%28sqrt%28n%29%29%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28n%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie replace every \"y\" with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%29 ALIGN=MIDDLE  ALT=\"sqrt%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29=%28sqrt%28n%2B1%29%29%5E2-%28sqrt%28n%29%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29=n%2B1-%28sqrt%28n%29%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: the square undoes the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29=n%2B1-n ALIGN=MIDDLE  ALT=\"%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29=n%2B1-n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%29 ALIGN=MIDDLE  ALT=\"sqrt%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: the square undoes the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29=1 ALIGN=MIDDLE  ALT=\"%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29=1 ALIGN=MIDDLE  ALT=\"%28sqrt%28n%2B1%29%2Bsqrt%28n%29%29%28sqrt%28n%2B1%29-sqrt%28n%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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