document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48951>Question 48951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to factor 6x^8yz - 48x^2y^7z<BR>\n" );
document.write( "I got 6x^2yz(-8x^7y^7)    <BR>\n" );
document.write( "Is this correct, or where did I go wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #32414 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=32414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you went wrong by forgetting the first term when you wrote the bracketed terms.\r<BR>\n" );
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document.write( "Factorising is all about converting something to \"two\" things multiplied.\r<BR>\n" );
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document.write( "Lets look at the starting terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x%5E8yz+-+48x%5E2y%5E7z+ ALIGN=MIDDLE  ALT=\"+6x%5E8yz+-+48x%5E2y%5E7z+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we should know what this really means, since a lot of this is shorthand used by mathematicians. What we really have is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6xxxxxxxxyz+-+48xxyyyyyyyz+ ALIGN=MIDDLE  ALT=\"+6xxxxxxxxyz+-+48xxyyyyyyyz+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or, further:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2A1xxxxxxxxyz+-+8%2A6xxyyyyyyyz+ ALIGN=MIDDLE  ALT=\"+6%2A1xxxxxxxxyz+-+8%2A6xxyyyyyyyz+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So to factor, we look at every term given... here we have just 2 terms, and we look for the most that is common to both.\r<BR>\n" );
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document.write( "So, start with the numbers. What is common? Answer is 6<BR>\n" );
document.write( "Now the x's. What is common? Answer is xx<BR>\n" );
document.write( "Now the y's. What is common? Answer is y<BR>\n" );
document.write( "and finally the z's. what is common? Answer is z\r<BR>\n" );
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document.write( "So we shall take out 6xxyz from both terms.\r<BR>\n" );
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document.write( "What is left from the first term? Answer is 1*xxxxxx --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E6+ ALIGN=MIDDLE  ALT=\"+x%5E6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And from the second term? Answer is 8yyyyyy --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8y%5E6+ ALIGN=MIDDLE  ALT=\"+8y%5E6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we had 6xxyz(1xxxxxx - 8yyyyyy) which is correct but not very \"professional\" in its look. So we write it in a more condensed manner as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x%5E2yz%28x%5E6+-+8y%5E6%29+ ALIGN=MIDDLE  ALT=\"+6x%5E2yz%28x%5E6+-+8y%5E6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And check: Multiply each of the terms in the bracket by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x%5E2xz+ ALIGN=MIDDLE  ALT=\"+6x%5E2xz+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you should arrive back at the question. So get used to checking.\r<BR>\n" );
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document.write( "Now the skill is to not need the xxxxxxxyz notation. You should be able to look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x%5E8yz+-+48x%5E2y%5E7z+ ALIGN=MIDDLE  ALT=\"+6x%5E8yz+-+48x%5E2y%5E7z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and factorise it into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x%5E2yz%28x%5E6+-+8y%5E6%29+ ALIGN=MIDDLE  ALT=\"+6x%5E2yz%28x%5E6+-+8y%5E6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in one line.\r<BR>\n" );
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document.write( "Now, knowing further maths skills we can spot something with the bracket:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E6+-+8y%5E6%29+ ALIGN=MIDDLE  ALT=\"+%28x%5E6+-+8y%5E6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be written as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E6+-+2%5E3%2Ay%5E6%29+ ALIGN=MIDDLE  ALT=\"+%28x%5E6+-+2%5E3%2Ay%5E6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28x%5E2%29%5E3+-+%282y%5E2%29%5E3+%29+ ALIGN=MIDDLE  ALT=\"+%28+%28x%5E2%29%5E3+-+%282y%5E2%29%5E3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And this is of the form of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E3+-+b%5E3+ ALIGN=MIDDLE  ALT=\"+a%5E3+-+b%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which factorises. I cannot remember this standard result, but your textbooks should quote this for you. That will give you an even more factorised version of the answer.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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