document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=94206>Question 94206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor Completely 12x^3-3xy^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68634 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=68634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "12x^3 - 3xy^2<BR>\n" );
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document.write( "First you can look for common factors in the two terms. Notice 3 is a common factor because<BR>\n" );
document.write( "it is a factor of 3 in the second term and a factor of 12 in the first term. The same can<BR>\n" );
document.write( "be said of x. It is a factor of x in the second term and a factor of x^3 in the first term.<BR>\n" );
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document.write( "So let's factor out 3x from both terms to get:<BR>\n" );
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document.write( "3x(4x^2 - y^2)<BR>\n" );
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document.write( "Now notice that the expression in the parentheses is the difference of two squares. That<BR>\n" );
document.write( "is, it can be written as [(2x)^2 - (y)^2].<BR>\n" );
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document.write( "This makes it fall under the factoring rule for the difference of two squares. This rule<BR>\n" );
document.write( "says that:<BR>\n" );
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document.write( "(A^2 - B^2) = (A - B)(A + B)<BR>\n" );
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document.write( "(You can multiply out the right side of this rule and it will help you to see why this<BR>\n" );
document.write( "rule is true.)<BR>\n" );
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document.write( "Comparing the left side of the rule to the terms you have in the brackets you can see<BR>\n" );
document.write( "that A = 2x and B = y.  So you can substitute 2x for every A on the right side of the rule<BR>\n" );
document.write( "and y for every B.  When you do that you get that [(2x)^2 - (y)^2] factors into (2x - y)(2x +y)<BR>\n" );
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document.write( "Putting this result together with the 3x we factored out earlier makes the factored<BR>\n" );
document.write( "result:<BR>\n" );
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document.write( "3x(2x - y)(2x + y)<BR>\n" );
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document.write( "and that's the answer to your problem.<BR>\n" );
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document.write( "Hope this helps you to see a way to go about factoring this problem and to get you familiar<BR>\n" );
document.write( "with the factoring rule for the difference between two squares.<BR>\n" );
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