document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93260>Question 93260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi there, <BR>\n" );
document.write( "I asked the following question before and I had a solution given to me, I do not understand some of it though, some guidance would be great.<BR>\n" );
document.write( "s=u.(v-u)/a + 1/2a((v-u)/a)^2 <BR>\n" );
document.write( "it should end up as v^2=u^2+2as \r<BR>\n" );
document.write( "\n" );
document.write( "first step was to multiply by 2a giving....<BR>\n" );
document.write( "2as=2u(v-u)+(v-u)^2\r<BR>\n" );
document.write( "\n" );
document.write( "expanding<BR>\n" );
document.write( "2as= 2uv-2u^2+v^2-2vu+u^2\r<BR>\n" );
document.write( "\n" );
document.write( "apparently by collecting terms this is equal to 2as=v^2-u^2, could someone please explain this last step for me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67896 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=67896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You were given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=u%28v-u%29%2Fa+%2B+%281%2F2%29%2Aa%2A%28%28v-u%29%2Fa%29%5E2%29 ALIGN=MIDDLE  ALT=\"s=u%28v-u%29%2Fa+%2B+%281%2F2%29%2Aa%2A%28%28v-u%29%2Fa%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You need to check the above and make sure this is the problem that you actually meant to<BR>\n" );
document.write( "have explained to you because that is the one that was worked out in the explanation you<BR>\n" );
document.write( "got.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "First you were told to multiply both sides (all terms) by 2a. The purpose of this multiplication<BR>\n" );
document.write( "was to eventually get rid of the denominators on the right side. It was performed as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2As+=+2a%2Au%28v-u%29%2Fa+%2B+%28%282a%2A1%29%2F2%29%2Aa%2A%28%28v-u%29%2Fa%29%5E2%29 ALIGN=MIDDLE  ALT=\"2a%2As+=+2a%2Au%28v-u%29%2Fa+%2B+%28%282a%2A1%29%2F2%29%2Aa%2A%28%28v-u%29%2Fa%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "On the right side in the second term multiply the \"a\" that is in the middle  times the <BR>\n" );
document.write( "numerator of the first factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2A1 ALIGN=MIDDLE  ALT=\"2a%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2 ALIGN=MIDDLE  ALT=\"2a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and makes<BR>\n" );
document.write( "the problem<BR>\n" );
document.write( "become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2As+=+2a%2Au%28v-u%29%2Fa+%2B+%28%282a%5E2%2A1%29%2F2%29%2A%28%28v-u%29%2Fa%29%5E2%29 ALIGN=MIDDLE  ALT=\"2a%2As+=+2a%2Au%28v-u%29%2Fa+%2B+%28%282a%5E2%2A1%29%2F2%29%2A%28%28v-u%29%2Fa%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now in the second term on the right side square out the last factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28v-u%29%2Fa%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28v-u%29%2Fa%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "by squaring both its numerator and denominator as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28v-u%29%2Fa%29%5E2%29=%28v-u%29%2Fa%2A%28v-u%29%2Fa+=+%28v%5E2-2uv+%2Bu%5E2%29%2Fa%5E2+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can now substitute the right side of this result in place of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28v-u%29%2Fa%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28v-u%29%2Fa%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in the problem, and the problem then becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2As+=+2a%2Au%28v-u%29%2Fa+%2B+%28%282a%5E2%2A1%29%2F2%29%2A%28%28v%5E2-2uv+%2Bu%5E2%29%2Fa%5E2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "At this point you can cancel the factors of 2a in the numerators with corresponding<BR>\n" );
document.write( "factors of 2a in the denominator as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2As+=+2%2A%28cross%28a%29%29%2Au%28v-u%29%2F%28cross%28a%29%29%2B%28%28%28cross%282%29%29%2A%28cross%28a%5E2%29%29%2A1%29%2F%28cross%282%29%29%29%2A%28%28v%5E2-2uv+%2Bu%5E2%29%2F%28cross%28a%5E2%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and you are left with:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2As+=+2u%28v-u%29%2Bv%5E2+-+2uv%2Bu%5E2 ALIGN=MIDDLE  ALT=\"2a%2As+=+2u%28v-u%29%2Bv%5E2+-+2uv%2Bu%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Doing the distributed multiplication of the first term on the right side results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2As+=+2uv+-+2u%5E2+%2Bv%5E2+-+2uv%2Bu%5E2 ALIGN=MIDDLE  ALT=\"2a%2As+=+2uv+-+2u%5E2+%2Bv%5E2+-+2uv%2Bu%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that on the right side you have terms that can be combined. The 2uv and the -2uv<BR>\n" );
document.write( "cancel each other and therefore, they disappear to leave you with:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2As+=+-2u%5E2+%2B+v%5E2+%2B+u%5E2 ALIGN=MIDDLE  ALT=\"2a%2As+=+-2u%5E2+%2B+v%5E2+%2B+u%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then the -2u^2 and the +u^2 combine to result in -u^2 and as a result the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2As+=+v%5E2+-+u%5E2+ ALIGN=MIDDLE  ALT=\"2a%2As+=+v%5E2+-+u%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and that's the result you are looking for. Hope this helps. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );