document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197177>Question 197177</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you explain to me how factoring 36x^2-100 = 4(3x-5)(3x+5) Its alittle confusing to me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147822 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=147822\">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=36x%5E2-100 ALIGN=MIDDLE  ALT=\"36x%5E2-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is difference of 2 squares (36x^2 is 6x*6x) and 100 is 10*10.\r<BR>\n" );
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document.write( "Usually that would be enough to say <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2-100 ALIGN=MIDDLE  ALT=\"36x%5E2-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x+-10%29%286x%2B10%29 ALIGN=MIDDLE  ALT=\"%286x+-10%29%286x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and call is a day. But in this case, you can see that each term includes a common factor of 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-10 ALIGN=MIDDLE  ALT=\"6x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%283x-5%29 ALIGN=MIDDLE  ALT=\"2%2A%283x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > etc.<BR>\n" );
document.write( "So <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x+-10%29%286x%2B10%29 ALIGN=MIDDLE  ALT=\"%286x+-10%29%286x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%283x-5%29+%2A+2%2A%283x%2B5%29 ALIGN=MIDDLE  ALT=\"2%2A%283x-5%29+%2A+2%2A%283x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2A%283x-5%29%2A%283x%2B5%29 ALIGN=MIDDLE  ALT=\"4+%2A%283x-5%29%2A%283x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Alternatively, you might have seen that 36 and 100 are both products of 2 squares.<BR>\n" );
document.write( "36 = 9*4 <BR>\n" );
document.write( "100 = 25*4<BR>\n" );
document.write( "If you factor out the 4, you are still left with a difference of 2 squares<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%289x%5E2+-+25%29 ALIGN=MIDDLE  ALT=\"4%2A%289x%5E2+-+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Which simplifies to the same result.\r<BR>\n" );
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document.write( "All this just confirms that in mathematics, there are many ways to get to the same answer (hopefully correct) answer.\r<BR>\n" );
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document.write( "Hope that helps\r<BR>\n" );
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document.write( " </SPAN>\n" );
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