document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198380>Question 198380</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with these two problems.<BR>\n" );
document.write( "Multiply  (5&#8730;3-15&#8730;5) (4&#8730;3+12&#8730;5)\r<BR>\n" );
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document.write( "Multiply and simplify ^3 sq rt y^4 * ^3 sq rt 16y^5<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148884 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=148884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Asqrt%283%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2B12%2Asqrt%285%29%29 ALIGN=MIDDLE  ALT=\"%285%2Asqrt%283%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2B12%2Asqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "Now let's FOIL the expression.\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%285%2Asqrt%283%29%29-15%2Asqrt%285%29%29%28highlight%284%2Asqrt%283%29%29%2B12%2Asqrt%285%29%29 ALIGN=MIDDLE   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=%285%2Asqrt%283%29%29%2A%284%2Asqrt%283%29%29=60 ALIGN=MIDDLE  ALT=\"%285%2Asqrt%283%29%29%2A%284%2Asqrt%283%29%29=60\"   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%285%2Asqrt%283%29%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2Bhighlight%2812%2Asqrt%285%29%29%29 ALIGN=MIDDLE   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=%285%2Asqrt%283%29%29%2A%2812%2Asqrt%285%29%29=60%2Asqrt%2815%29 ALIGN=MIDDLE  ALT=\"%285%2Asqrt%283%29%29%2A%2812%2Asqrt%285%29%29=60%2Asqrt%2815%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=%285%2Asqrt%283%29%2Bhighlight%28-15%2Asqrt%285%29%29%29%28highlight%284%2Asqrt%283%29%29%2B12%2Asqrt%285%29%29 ALIGN=MIDDLE   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=%28-15%2Asqrt%285%29%29%2A%284%2Asqrt%283%29%29=-60%2Asqrt%2815%29 ALIGN=MIDDLE  ALT=\"%28-15%2Asqrt%285%29%29%2A%284%2Asqrt%283%29%29=-60%2Asqrt%2815%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=%285%2Asqrt%283%29%2Bhighlight%28-15%2Asqrt%285%29%29%29%284%2Asqrt%283%29%2Bhighlight%2812%2Asqrt%285%29%29%29 ALIGN=MIDDLE   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=%28-15%2Asqrt%285%29%29%2A%2812%2Asqrt%285%29%29=-900 ALIGN=MIDDLE  ALT=\"%28-15%2Asqrt%285%29%29%2A%2812%2Asqrt%285%29%29=-900\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "---------------------------------------------------\r<BR>\n" );
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document.write( "So we have the terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Asqrt%2815%29 ALIGN=MIDDLE  ALT=\"60%2Asqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-60%2Asqrt%2815%29 ALIGN=MIDDLE  ALT=\"-60%2Asqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-900 ALIGN=MIDDLE  ALT=\"-900\"   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=60%2B60%2Asqrt%2815%29-60%2Asqrt%2815%29-900 ALIGN=MIDDLE  ALT=\"60%2B60%2Asqrt%2815%29-60%2Asqrt%2815%29-900\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add every term listed above 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=-840 ALIGN=MIDDLE  ALT=\"-840\"   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=%285%2Asqrt%283%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2B12%2Asqrt%285%29%29 ALIGN=MIDDLE  ALT=\"%285%2Asqrt%283%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2B12%2Asqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOILs to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-840 ALIGN=MIDDLE  ALT=\"-840\"   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=%285%2Asqrt%283%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2B12%2Asqrt%285%29%29=-840 ALIGN=MIDDLE  ALT=\"%285%2Asqrt%283%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2B12%2Asqrt%285%29%29=-840\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cy%5E4%29%2Aroot%283%2C16y%5E5%29 ALIGN=MIDDLE  ALT=\"root%283%2Cy%5E4%29%2Aroot%283%2C16y%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cy%5E4%2A16y%5E5%29 ALIGN=MIDDLE  ALT=\"root%283%2Cy%5E4%2A16y%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C16y%5E9%29 ALIGN=MIDDLE  ALT=\"root%283%2C16y%5E9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C8%2A2%2Ay%5E9%29 ALIGN=MIDDLE  ALT=\"root%283%2C8%2A2%2Ay%5E9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 16 to get 8*2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C8%2A2%2A%28y%5E3%29%5E3%29 ALIGN=MIDDLE  ALT=\"root%283%2C8%2A2%2A%28y%5E3%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E9 ALIGN=MIDDLE  ALT=\"y%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E3%29%5E3 ALIGN=MIDDLE  ALT=\"%28y%5E3%29%5E3\"   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=root%283%2C8%29%2Aroot%283%2C2%29%2Aroot%283%2C%28y%5E3%29%5E3%29 ALIGN=MIDDLE  ALT=\"root%283%2C8%29%2Aroot%283%2C2%29%2Aroot%283%2C%28y%5E3%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C2%29%2Aroot%283%2C%28y%5E3%29%5E3%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C2%29%2Aroot%283%2C%28y%5E3%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the cube root of 8 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C2%29%2Ay%5E3 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C2%29%2Ay%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the cube root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E3%29%5E3 ALIGN=MIDDLE  ALT=\"%28y%5E3%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3 ALIGN=MIDDLE  ALT=\"y%5E3\"   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=2y%5E3%2Aroot%283%2C2%29 ALIGN=MIDDLE  ALT=\"2y%5E3%2Aroot%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cy%5E4%29%2Aroot%283%2C16y%5E5%29=2y%5E3%2Aroot%283%2C2%29 ALIGN=MIDDLE  ALT=\"root%283%2Cy%5E4%29%2Aroot%283%2C16y%5E5%29=2y%5E3%2Aroot%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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