document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636668>Question 636668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show all work. Find the quotient: (16a^2 -b^2)/(4a -b) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401170 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=401170\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The term 16a^2 can be expessed as 4^2*a^2. Using the property that the product of two squares is equal to the square of the products, 16a^2 can be expressed as (4a)^2. Then the numerator is the difference of two perfect squares (4a)^2 and b^2, therefore can be factored into the product of the sum and difference  of the numbers being squared. In this case we have <BR>\n" );
document.write( "{(4a)^2 - b^2} = (4a + b)(4a - b)<BR>\n" );
document.write( "You can check this factorization by \"FOIL\",<BR>\n" );
document.write( " (4a)*(4a) -4ab +4ab - b*b = (4a)^2 - b^2 =  16a^2 - b^2<BR>\n" );
document.write( "Note that the \"OI\" terms of \"FOIL\" cancel. This does not happen when the two perfect squares are added.\r<BR>\n" );
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document.write( "Rewriting the given expression yields<BR>\n" );
document.write( "  {(4a + b)(4a - b)}/(4a - b)<BR>\n" );
document.write( "which simplifies to the quotient<BR>\n" );
document.write( "   4a + b<BR>\n" );
document.write( " </SPAN>\n" );
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