document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003557>Question 1003557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor 15m^3n +20mn^2 -10m^2n  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620251 by </B><A HREF=/tutors/aboutme.mpl?userid=smithsac><B>smithsac(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=smithsac><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=620251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To Factor simply start with GCF(greatest common factor)for each number and letter:\r<BR>\n" );
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document.write( "so taking the whole numbers first: 15, 20, 10  \r<BR>\n" );
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document.write( "There GCF is the number 5  (like 5x3 = 15   5x4=20    5x2=10)  all have the factor 5\r<BR>\n" );
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document.write( "ok, so we will USE THE NUMBER 5 for the first digit to our answer\r<BR>\n" );
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document.write( "Next, look at the first letter which is m {the first m is m^3, the second m is simply just m, the third m is m^2}\r<BR>\n" );
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document.write( "Based on the number of exponents the GCF for m is m (like m*m*m = m^3,  m*1=m   then m*m = m^   they all have at least one m in common)\r<BR>\n" );
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document.write( "So our SECOND digit after 5 is now m \r<BR>\n" );
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document.write( "Do the same thing with the letter n:<BR>\n" );
document.write( "First one is n, second is n^2 and the third is n (n*1, n*n, n*1   -  they all have at least one n in common)\r<BR>\n" );
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document.write( "SO OUR Third digit after 5m is n\r<BR>\n" );
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document.write( "So now using 5mn we figure out the rest which is put into parenthesis:\r<BR>\n" );
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document.write( "working backwards from your original equation above we see 15m^3n is now split up as 5mn(3m^2) [This means if we were to multiply - the answer would result with 15m^3n]  \r<BR>\n" );
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document.write( "So now we do the same with 20mn^2 is now split up as 5mn(4n)\r<BR>\n" );
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document.write( "Then finally 10m^2n is now split up as 5mn(2m)\r<BR>\n" );
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document.write( "Putting these all together we get the answer as\r<BR>\n" );
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document.write( "5mn(3m^2 + 4n - 2m)\r<BR>\n" );
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document.write( "To see if you're correct, simply do the distributive property and you'll see you'll end up with original equation which means you factored it correctly. </SPAN>\n" );
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