document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=903107>Question 903107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a math book I am using / reading the author states that the expression n + (n-3) simplifies to n(n-1). But he does not show steps for this or give an explanation.\r<BR>\n" );
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document.write( "I checked the expression on many web-based math sites (including your site) and none show the simplification of the original expression as n(n-1).\r<BR>\n" );
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document.write( "One site states that n + (n-3) simplifies to the following expression (with steps shown):<BR>\n" );
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document.write( "Simplifying<BR>\n" );
document.write( "n + n(n + -3)\r<BR>\n" );
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document.write( "Reorder the terms:<BR>\n" );
document.write( "n + n(-3 + n)<BR>\n" );
document.write( "n + (-3 * n + n * n)<BR>\n" );
document.write( "n + (-3n + n2)\r<BR>\n" );
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document.write( "Combine like terms: n + -3n = -2n<BR>\n" );
document.write( "-2n + n2<BR>\n" );
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document.write( "Can you state whether the expression n + n(n-3) can simplify to n(n-1) and if so, can you please show the steps.\r<BR>\n" );
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document.write( "Thank you in advance.\r<BR>\n" );
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document.write( "Greg </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #547796 by </B><A HREF=/tutors/aboutme.mpl?userid=AlgebraLady88><B>AlgebraLady88(44)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AlgebraLady88><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=AlgebraLady88><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=547796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ok, let's take a look at the equation\r<BR>\n" );
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document.write( "n + n (n- 3)\r<BR>\n" );
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document.write( "For the part  n (n +3) , we can express this using the Distributive Postulate. A postulate is a statement that is true. The Distributive method is as follows:\r<BR>\n" );
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document.write( "a (b + c) = ab + ac\r<BR>\n" );
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document.write( "We take the 'a' and multiply it with the 'b' which gives us ab plus the 'a' multiplied by the 'c,' which gives us ac\r<BR>\n" );
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document.write( "So, n + n ( n-3) = n + n ^ 2 - 3n = n^2 - 2n = n (n -2)\r<BR>\n" );
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document.write( "It will not simplify to n (n-1) . \r<BR>\n" );
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document.write( "\" One item I should have asked about this expression.  If the simplified expression n(n-2) is put over denominator of 2, would this then simplify to n(n-1)  ??\"\r<BR>\n" );
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document.write( "The answer is no. Here's why. You can only cancel factors , not terms in a polynomial. Let me explain .\r<BR>\n" );
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document.write( "2n/2 * n/2 =  n^2/2    Correct \r<BR>\n" );
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document.write( "(2n + 5)/ 2 = n + 5    Incorrect ( You cannot cancel the 2's and get n+5)\r<BR>\n" );
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document.write( "So, for  [n(n-2)]/2 , your answer would still be [n(n-2])/2 because there are no factors to cancel.\r<BR>\n" );
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document.write( "You can alternately do this:\r<BR>\n" );
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document.write( "[n(n-2)]/2 = (n^2-2n)/2= n^2/2 -2n/2 =  n^2/2 - n \r<BR>\n" );
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document.write( "You are getting rid of the parenthesis and then putting each term over the same denominator.  The two terms are n^2 and -2n . You put each over the denominator  2. Then you can reduce each separate fraction where applicable.However, it does make things more complicated. This topic comes under<BR>\n" );
document.write( "'simplifying rational expressions.\"\r<BR>\n" );
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document.write( " </SPAN>\n" );
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