document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73970>Question 73970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify: 3x^2 (4x^2 - 2x + 3)<BR>\n" );
document.write( "A) 12x^4 - 6x^3 + 9x^2 <BR>\n" );
document.write( "B) 7x^2 + x + 6 <BR>\n" );
document.write( "C) 7x^4 - 6x^3 + 6x^2 <BR>\n" );
document.write( "D) x^2 - 2x + 3 <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52978 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=52978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x^2 (4x^2 - 2x + 3)<BR>\n" );
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document.write( "The purpose of this problem is to teach you a couple of rules about algebraic multiplication.<BR>\n" );
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document.write( "These rules are that you multiply the leading numbers (called coefficients) and add the<BR>\n" );
document.write( "exponents of the like variables.  In this case there is only the variable x.  And remember that<BR>\n" );
document.write( "x^2 has an exponent of 2 and just plain x has a variable of 1.<BR>\n" );
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document.write( "On to the multiplication.<BR>\n" );
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document.write( "The 3x^2 multiplies each of the 3 terms in the parentheses.<BR>\n" );
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document.write( "The first multiplication is 3x^2 times 4x^2.  Multiply the 3 times the 4 to get 12.  Then you <BR>\n" );
document.write( "multiply x^2 times x^2 by just adding the exponents to get x^4.  So the result of multiplying<BR>\n" );
document.write( "3x^2 by 4x^2 is 12x^4.<BR>\n" );
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document.write( "The second multiplication is 3x^2 times -2x. The -2x should be thought of as -2x^1.<BR>\n" );
document.write( "Multiply the 3 times the -2 to get -6 and multiply the x^2 times x^1 by adding the exponents<BR>\n" );
document.write( "of 2 and 1 to get x^3.  So the combined multiplication results in -6x^3.<BR>\n" );
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document.write( "Finally the last of the three multiplications is to multiply 3x^2 times +3. This time<BR>\n" );
document.write( "all you need to do is multiply the 3 times the +3 to get 9 and the x^2 tags along to<BR>\n" );
document.write( "make this answer +9x^2.<BR>\n" );
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document.write( "Putting all 3 answers together gives you the combined answer of 12x^4 -6x^3 + 9x^2.<BR>\n" );
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document.write( "Answer A is the correct answer.<BR>\n" );
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document.write( "I hope this helps you to see how to work this problem and that you can see how to apply a<BR>\n" );
document.write( "couple of basic rules of algebraic multiplication to get the answer.  The important thing<BR>\n" );
document.write( "here is to understand what is going on. </SPAN>\n" );
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