document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=415037>Question 415037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a^2+5ab+6b^2/a^2-5ab+6b^2) * (10a-30b/5a+10b) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #291017 by </B><A HREF=/tutors/aboutme.mpl?userid=woolybear><B>woolybear(13)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=woolybear><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=woolybear><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=291017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If simplify this what you come up with.<BR>\n" );
document.write( "(a^(2)+5ab+(6b^(2))/(a^(2))-5ab+6b^(2))*(10a-(30b)/(5)*a+10b)\r<BR>\n" );
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document.write( "Since 5ab and -5ab are like terms, add -5ab to 5ab to get 0.<BR>\n" );
document.write( "(a^(2)+(6b^(2))/(a^(2))+6b^(2))*(10a-(30b)/(5)*a+10b)\r<BR>\n" );
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document.write( "To add fractions, the denominators must be equal.  The denominators can be made equal by finding the least common denominator (LCD).  In this case, the LCD is a^(2).  Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.<BR>\n" );
document.write( "(a^(2)*(a^(2))/(a^(2))+(6b^(2))/(a^(2))+6b^(2)*(a^(2))/(a^(2)))*(10a-(30b)/(5)*a+10b)\r<BR>\n" );
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document.write( "Complete the multiplication to produce a denominator of a^(2) in each expression.<BR>\n" );
document.write( "((a^(4))/(a^(2))+(6b^(2))/(a^(2))+(6a^(2)b^(2))/(a^(2)))*(10a-(30b)/(5)*a+10b)\r<BR>\n" );
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document.write( "Combine the numerators of all expressions that have common denominators.<BR>\n" );
document.write( "((a^(4)+6b^(2)+6a^(2)b^(2))/(a^(2)))*(10a-(30b)/(5)*a+10b)\r<BR>\n" );
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document.write( "Reorder the polynomial a^(4)+6b^(2)+6a^(2)b^(2) alphabetically from left to right, starting with the highest order term.<BR>\n" );
document.write( "((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2)))*(10a-(30b)/(5)*a+10b)\r<BR>\n" );
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document.write( "Reduce the expression -(30b)/(5) by removing a factor of 5 from the numerator and denominator.<BR>\n" );
document.write( "((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2)))*(10a-6b*a+10b)\r<BR>\n" );
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document.write( "Multiply -6b by a to get -6ab.<BR>\n" );
document.write( "((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2)))*(10a-6ab+10b)\r<BR>\n" );
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document.write( "Reorder the polynomial 10a-6ab+10b alphabetically from left to right, starting with the highest order term.<BR>\n" );
document.write( "((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2)))*(-6ab+10a+10b)\r<BR>\n" );
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document.write( "Multiply each term in the first polynomial by each term in the second polynomial.<BR>\n" );
document.write( "((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2))*-6ab+(a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2))*10a+(a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2))*10b)\r<BR>\n" );
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document.write( "Multiply ((a^(4)+6a^(2)b^(2)+6b^(2)))/(a^(2)) by each term in -6ab+10a+10b to get -(2(3a^(5)b+18a^(3)b^(3)-5a^(5)-30a^(3)b^(2)-5a^(4)b-30a^(2)b^(3)+18ab^(3)-30ab^(2)-30b^(3)))/(a^(2)).<BR>\n" );
document.write( "(-(2(3a^(5)b+18a^(3)b^(3)-5a^(5)-30a^(3)b^(2)-5a^(4)b-30a^(2)b^(3)+18ab^(3)-30ab^(2)-30b^(3)))/(a^(2)))\r<BR>\n" );
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document.write( "Remove the parentheses around the expression -(2(3a^(5)b+18a^(3)b^(3)-5a^(5)-30a^(3)b^(2)-5a^(4)b-30a^(2)b^(3)+18ab^(3)-30ab^(2)-30b^(3)))/(a^(2)).<BR>\n" );
document.write( "-(2(3a^(5)b+18a^(3)b^(3)-5a^(5)-30a^(3)b^(2)-5a^(4)b-30a^(2)b^(3)+18ab^(3)-30ab^(2)-30b^(3)))/(a^(2)) </SPAN>\n" );
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