document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=547170>Question 547170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely:\r<BR>\n" );
document.write( "\n" );
document.write( "4y^2-12y+9-z^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, I tried but I'm stuck. Here's my work so far.\r<BR>\n" );
document.write( "\n" );
document.write( "(4y^2-z^2)+(9-12y)<BR>\n" );
document.write( "(2y-z)^2 + 3(3-4y)\r<BR>\n" );
document.write( "\n" );
document.write( "I'm not sure if it's at all correct. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356277 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=356277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You were on the right track.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Given to factor:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2-12y%2B9-z%5E2+ ALIGN=MIDDLE  ALT=\"4y%5E2-12y%2B9-z%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Separate the first three terms as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%5E2-12y+%2B+9%29+-+z%5E2 ALIGN=MIDDLE  ALT=\"%284y%5E2-12y+%2B+9%29+-+z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that the terms in the parentheses are an algebraic expression that is a perfect square. It can be factored as shown below:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y+-+3%29%5E2+-z%5E2 ALIGN=MIDDLE  ALT=\"%282y+-+3%29%5E2+-z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice now that this new form is the difference between two squares. Recall the rule for the difference of two squares:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2+=+%28a+-+b%29%2A%28a%2Bb%29+ ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2+=+%28a+-+b%29%2A%28a%2Bb%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "For your problem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%282y-3%29 ALIGN=MIDDLE  ALT=\"a+=+%282y-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+z ALIGN=MIDDLE  ALT=\"b+=+z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute these into the rule for the difference of two squares as shown in the steps that follow:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2+=+%28a+-+b%29%2A%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2+=+%28a+-+b%29%2A%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y-3%29%5E2+-+z%5E2+=+%28%282y+-+3%29-z%29%2A%28%282y+-+3%29%2Bz%29 ALIGN=MIDDLE  ALT=\"%282y-3%29%5E2+-+z%5E2+=+%28%282y+-+3%29-z%29%2A%28%282y+-+3%29%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Remove the interior parentheses on the right side of this equation and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y-3%29%5E2+-+z%5E2+=+%282y+-+3-z%29%2A%282y+-+3%2Bz%29 ALIGN=MIDDLE  ALT=\"%282y-3%29%5E2+-+z%5E2+=+%282y+-+3-z%29%2A%282y+-+3%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The right side is the factored form of the problem that you were given. So you can write the answer to this problem in the equation form:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2-12y%2B9-z%5E2+=+%282y+-+3-z%29%2A%282y+-+3%2Bz%29 ALIGN=MIDDLE  ALT=\"4y%5E2-12y%2B9-z%5E2+=+%282y+-+3-z%29%2A%282y+-+3%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "or maybe you want to rearrange the terms in the parentheses a little so the letters come first as in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2-12y%2B9-z%5E2+=+%282y-z+-+3%29%2A%282y+%2Bz-+3%29 ALIGN=MIDDLE  ALT=\"4y%5E2-12y%2B9-z%5E2+=+%282y-z+-+3%29%2A%282y+%2Bz-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Whatever your teacher prefers. It's just a matter of preference, but the rearrangement is probably the most commonly used form. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you understand the problem a little better.<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );