document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=920810>Question 920810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have two problems with factorization. I tried everything, in many ways, but can't find the right answer.\r<BR>\n" );
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document.write( "First:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E3+%2B+8 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E3+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The answer is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x%5E2-4x%2B7%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x%5E2-4x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Second:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2Bx%5E2y%5E2%2By%5E4 ALIGN=MIDDLE  ALT=\"x%5E4%2Bx%5E2y%5E2%2By%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bxy%2By%5E2%29%28x%5E2-xy%2By%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bxy%2By%5E2%29%28x%5E2-xy%2By%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558586 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=558586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) We can factor the sum of cubes using the following formula:<BR>\n" );
document.write( "x^3 + y^3 = (x+y)(x^2-xy+y^2)<BR>\n" );
document.write( "we are given (x-1)^3 + 2^3<BR>\n" );
document.write( "therefore we get<BR>\n" );
document.write( "(x-1+2)((x-1)^2 -(x-1)2 +4))<BR>\n" );
document.write( "(x+1)(x^2-2x+1 -2x +2 +4)<BR>\n" );
document.write( "(x+1)(x^2 -4x +7)<BR>\n" );
document.write( "2) Let a = x^2<BR>\n" );
document.write( "Let b = y^2.<BR>\n" );
document.write( "So lets substitute the values of a and b in for x^2 and y^2:<BR>\n" );
document.write( "a^2 + ab + y^2<BR>\n" );
document.write( "If you know that (a + b)^2 = a^2 + 2ab + b^2, then you can see that the two expressions are similar.<BR>\n" );
document.write( "lets just add one set of \"ab\" to the first equation, so that we get a^2 + 2ab + b^2, which is easily simplified.<BR>\n" );
document.write( "therefore, we would get:<BR>\n" );
document.write( "(a + b)^2 - ab <----if we added ab, we must now subtract it.<BR>\n" );
document.write( "now, just substitute the values of a and b back in:<BR>\n" );
document.write( "(x^2 + y^2)^2 - x^2y^2 then apply the difference of squares here.<BR>\n" );
document.write( "(x^2 + y^2) - (xy)^2<BR>\n" );
document.write( "(x ^2 + y^2 + xy) (x^2 + y^2 - xy)  </SPAN>\n" );
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