document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134877>Question 134877</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0030358299/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Factor:\r<BR>\n" );
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document.write( "3x^3+81 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98772 by </B><A HREF=/tutors/aboutme.mpl?userid=nycsharkman><B>nycsharkman(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nycsharkman><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=98772\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factor:\r<BR>\n" );
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document.write( "3x^3+81\r<BR>\n" );
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document.write( "We have the sum of cubes.\r<BR>\n" );
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document.write( "We use this formula:\r<BR>\n" );
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document.write( "x^3 + y^3 = (x+y)(x^2-xy+y^2)\r<BR>\n" );
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document.write( "First thing you want to do is factor out 3.\r<BR>\n" );
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document.write( "3(x^3 + 27)...In other words, 3x^3 divided by 3 = x^3 and 81 divided by 3 = 27 (in case you are wondering where those numbers came from).\r<BR>\n" );
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document.write( "We now factor the sum of cubes listed in the parentheses.\r<BR>\n" );
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document.write( "Write 27 using base 3.\r<BR>\n" );
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document.write( "3^3 = 27\r<BR>\n" );
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document.write( "We now have:\r<BR>\n" );
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document.write( "3(x^3 + 3^3)\r<BR>\n" );
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document.write( "Base x and 3 = base x and y in the above formula.\r<BR>\n" );
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document.write( "Here comes the easy part.\r<BR>\n" );
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document.write( "We plug and chug.\r<BR>\n" );
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document.write( "x^3 + y^3 = (x+y)(x^2-xy+y^2)....This is the formula for the sum of cubes.\r<BR>\n" );
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document.write( "3(x^3 + 3^3) = 3(x + 3)(x^2 - 3y + 3^2)\r<BR>\n" );
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document.write( "3(x^3 + 3^3) = 3(x + 3)(x^2 - 3y + 9)\r<BR>\n" );
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document.write( "The original question actually breaks into 3 factors:\r<BR>\n" );
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document.write( "3, (x + 3) and (x^2 - 3y + 9)\r<BR>\n" );
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document.write( "Final answer:  \r<BR>\n" );
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document.write( "3(x + 3)(x^2 - 3y + 9)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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