document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051736>Question 1051736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Multiply as indicated and simplify\r<BR>\n" );
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document.write( "(4n + 7)(n^2 - 7n - 7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667214 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are using the distributive law of multiplication.\r<BR>\n" );
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document.write( "the law states:\r<BR>\n" );
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document.write( "a*(b+c) = a*b + a*c\r\n" );
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document.write( "a*(b+c+d) = a*b + a*c + a*d\r\n" );
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document.write( "(a+b)*c = a*c + b*c\r\n" );
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document.write( "(a+b)*(c+d) = a*c + a*d\r\n" );
document.write( "            + b*c + b*d\r\n" );
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document.write( "(a+b)*(c+d+e) = a*c + a*d + a*e\r\n" );
document.write( "              + b*c + b*d + b*e\r\n" );
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document.write( "it works with negative values as well.\r\n" );
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document.write( "for example:\r\n" );
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document.write( "(a-b)*(c+d+e) = a*c + a*d + a*e\r\n" );
document.write( "              - b*c - b*d - b*e\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "dealing with the negatives is the hardest part.<BR>\n" );
document.write( "you have to be very careful not to screw something up.\r<BR>\n" );
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document.write( "using the distributive law, i would solve your problem in the following manner:\r<BR>\n" );
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document.write( "(4n + 7)*(n^2 - 7n - 7) = 4n*n^2 + 4n*-7n + 4n*-7\r\n" );
document.write( "                        + 7*n^2  + 7*-7n  + 7*-7\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "what you are looking at is then:\r<BR>\n" );
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document.write( "(4n + 7)*(n^2 - 7n - 7) = 4n*n^2 + 4n*-7n + 4n*-7 + 7*n^2 + 7*-7n + 7*-7\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "(4n + 7)*(n^2 - 7n - 7) = 4n^3 - 28n^2 -28n + 7n^2 - 49n -49\r<BR>\n" );
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document.write( "now you want to combine like terms to get:\r<BR>\n" );
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document.write( "(4n + 7)*(n^2 - 7n - 7) = 4n^3 - 21n^2 -77n -49\r<BR>\n" );
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document.write( "what's left is to confirm you did it right.\r<BR>\n" );
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document.write( "what i usually do is take a random value of the variable and then analyze both the original expression and the final expression to see that the answer is the same.\r<BR>\n" );
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document.write( "if it is, i probably did good.<BR>\n" );
document.write( "if it isn't, i go back and see what i did wrong.\r<BR>\n" );
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document.write( "i will take a random value of n as 20.<BR>\n" );
document.write( "i picked a nice round number to make the calculations easier.\r<BR>\n" );
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document.write( "my equation is:\r<BR>\n" );
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document.write( "(4n + 7)*(n^2 - 7n - 7) = 4n^3 - 21n^2 -77n -49\r<BR>\n" );
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document.write( "i evaluate the expression on the left of the equal sign and then i evaluate    the expression on the right side of the equal side, using 20 as my value for n.\r<BR>\n" );
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document.write( "(4n + 7) * (n^2 - 7n - 7) becomes (4*20 + 7) * (20^2 - 7*20 - 7).<BR>\n" );
document.write( "the result is equal to 22011\r<BR>\n" );
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document.write( "4n^3 - 21n^2 - 77n - 49 becomes 4*20^3 - 21*20^2 - 77*20 - 49.<BR>\n" );
document.write( "the result is equal to 22011.\r<BR>\n" );
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document.write( "the results are the same, so i assume that i applied the distributive law to the original equation correctly.\r<BR>\n" );
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document.write( "my final expression is 4n^3 - 21n^2 -77n -49\r<BR>\n" );
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document.write( " </SPAN>\n" );
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