document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165809>Question 165809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would you solve the following equation by factoring and applying the Zero-Product Property?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-81=0 ALIGN=MIDDLE  ALT=\"x%5E4-81=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122219 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122219\">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%5E4-81 ALIGN=MIDDLE  ALT=\"x%5E4-81\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same thing as saying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%5E2-9%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%5E2-9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  You may be familiar with the special rule for factoring \"the difference of 2 perfect squares\"<BR>\n" );
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document.write( "The difference of two perfect squares is as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2=%28a-b%29%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2=%28a-b%29%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this can be proven true by foiling (a-b)(a+b)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bab-ab-b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bab-ab-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So...in this equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%5E2-9%5E2=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%5E2-9%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=x%5E2 ALIGN=MIDDLE  ALT=\"a=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=9 ALIGN=MIDDLE  ALT=\"b=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so (x^2-9)(x^2+9)=0<BR>\n" );
document.write( "the Zero-Product Property says that when 2 numbers are multiplied together, if either number is zero, then the product will be zero.<BR>\n" );
document.write( "so<BR>\n" );
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document.write( "the equation will be true when (x^2-9)=0 or when (x^2+9)=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-9=0 ALIGN=MIDDLE  ALT=\"x%5E2-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 9 to each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=9 ALIGN=MIDDLE  ALT=\"x%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "take the square root of each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B-3 ALIGN=MIDDLE  ALT=\"x=%2B-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B9=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 9 from each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-9 ALIGN=MIDDLE  ALT=\"x%5E2=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "take the square root of each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=SQRT%28-9%29 ALIGN=MIDDLE  ALT=\"x=SQRT%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > since we are unable to take the square root of a negative number, this is not a real solution.<BR>\n" );
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document.write( "so<BR>\n" );
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document.write( "The final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B-3 ALIGN=MIDDLE  ALT=\"x=%2B-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > but the question is asking for all of the above work.<BR>\n" );
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document.write( "Tutoring available<BR>\n" );
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