document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180262>Question 1180262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show all work. Be sure to answer both part A and B to the following questions.\r<BR>\n" );
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document.write( "Part A, Which of the following is a polynomial equation? \r<BR>\n" );
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document.write( "a.6x^2 + x + 2 = (6x-2)(x+4)<BR>\n" );
document.write( "b.(5x-1)^2 = 25x^2 + 1 <BR>\n" );
document.write( "c.9(4a^2 - 4ab + b^2) = (6a - 3b)^2<BR>\n" );
document.write( "d.(7x + 2)(x - y) = 7x(x - y) - 2y\r<BR>\n" );
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document.write( "Part B, Which expression is not equivalent to 16x^4 - y^4?\r<BR>\n" );
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document.write( "a.(2x-y)(2x+y)(4x^2 + y^2)<BR>\n" );
document.write( "b.(2x)^4 - (y)^4<BR>\n" );
document.write( "c.4x^2(4x^2 - y^2) + y^2(4x^2 - y^2)<BR>\n" );
document.write( "d.(2x-y)(8x^3 + y^3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809876 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> recall: \r<BR>\n" );
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document.write( "A polynomial function is a function that involves only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=non-negative ALIGN=MIDDLE  ALT=\"non-negative\"   DISABLED_style= \"max-width:90%; height:auto;\" > integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=powers ALIGN=MIDDLE  ALT=\"powers\"   DISABLED_style= \"max-width:90%; height:auto;\" > or only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive ALIGN=MIDDLE  ALT=\"positive\"   DISABLED_style= \"max-width:90%; height:auto;\" > integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=exponents ALIGN=MIDDLE  ALT=\"exponents\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a variable in an equation like the quadratic equation, cubic equation, etc. For example, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5 ALIGN=MIDDLE  ALT=\"2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a polynomial.  As a general rule of thumb if an algebraic expression has a radical in it then it isn't a polynomial.<BR>\n" );
document.write( "A zero polynomial is the one where all the coefficients are equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zero ALIGN=MIDDLE  ALT=\"zero\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So, the degree of the zero polynomial is either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=undefined ALIGN=MIDDLE  ALT=\"undefined\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or it is set equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "A polynomial function is made up of terms called monomials.\r<BR>\n" );
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document.write( "A monomial is an expression that contains only one term. In other words, a monomial is a polynomial with a single term. Generally, monomials include numbers, variables, or a number and a variable multiplied together, two or more variables multiplied together. A monomial is an expression that does not contain any arithmetic operators.\r<BR>\n" );
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document.write( "Part A\r<BR>\n" );
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document.write( "a.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2+%2B+x+%2B+2+=+%286x-2%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"6x%5E2+%2B+x+%2B+2+=+%286x-2%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....expand<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2+%2B+x+%2B+2+=+6+x%5E2+%2B+22+x-8 ALIGN=MIDDLE  ALT=\"6x%5E2+%2B+x+%2B+2+=+6+x%5E2+%2B+22+x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%286x%5E2%29+%2B+x+%2B+2+=+cross%286+x%5E2%29+%2B+22+x+-8 ALIGN=MIDDLE  ALT=\"cross%286x%5E2%29+%2B+x+%2B+2+=+cross%286+x%5E2%29+%2B+22+x+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+2+=++22+x+-8 ALIGN=MIDDLE  ALT=\"x+%2B+2+=++22+x+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=++22+x-x-2+-8 ALIGN=MIDDLE  ALT=\"0+=++22+x-x-2+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=++21x-10 ALIGN=MIDDLE  ALT=\"0+=++21x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> polynomial\r<BR>\n" );
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document.write( "b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-1%29%5E2+=+25x%5E2+%2B+1 ALIGN=MIDDLE  ALT=\"%285x-1%29%5E2+=+25x%5E2+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >....expand<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2+-+10x+%2B+1+=+25x%5E2+%2B+1 ALIGN=MIDDLE  ALT=\"25x%5E2+-+10x+%2B+1+=+25x%5E2+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2825x%5E2%29+-+10+x+%2B+1+=+cross%2825x%5E2+%29%2B+1 ALIGN=MIDDLE  ALT=\"cross%2825x%5E2%29+-+10+x+%2B+1+=+cross%2825x%5E2+%29%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+10+x+%2B+1+=++1 ALIGN=MIDDLE  ALT=\"-+10+x+%2B+1+=++1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+10+x+%2B+1-1+=++0 ALIGN=MIDDLE  ALT=\"-+10+x+%2B+1-1+=++0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+10x++=++0 ALIGN=MIDDLE  ALT=\"-+10x++=++0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x++=++0 ALIGN=MIDDLE  ALT=\"x++=++0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> is polynomial =>classification: a degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > polynomial with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > term and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > variable\r<BR>\n" );
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document.write( "c.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%284a%5E2+-+4ab+%2B+b%5E2%29+=+%286a+-+3b%29%5E2 ALIGN=MIDDLE  ALT=\"9%284a%5E2+-+4ab+%2B+b%5E2%29+=+%286a+-+3b%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....expand<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2836a%5E2%29+-+cross%2836ab+%29%2Bcross%28+9b%5E2%29=+cross%2836a%5E2%29+-+cross%2836ab%29+%2B+cross%289b%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >........simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>  is polynomial =>classification: is a degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > polynomial with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > term and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > variable\r<BR>\n" );
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document.write( "d.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x+%2B+2%29%28x+-+y%29+=+7x%28x+-+y%29+-+2y ALIGN=MIDDLE  ALT=\"%287x+%2B+2%29%28x+-+y%29+=+7x%28x+-+y%29+-+2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >....expand<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2+-+7xy+%2B+2x+-+2y+=+7x%5E2+-+7xy+-+2y ALIGN=MIDDLE  ALT=\"7x%5E2+-+7xy+%2B+2x+-+2y+=+7x%5E2+-+7xy+-+2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >........simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%287x%5E2%29+-+cross%287xy%29+%2B+2x+-cross%28+2y+%29=+cross%287x%5E2%29+-+cross%287xy%29+-+cross%282y%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+=+0 ALIGN=MIDDLE  ALT=\"+2x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+0 ALIGN=MIDDLE  ALT=\"+x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> is a degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > polynomial with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > term and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > variable\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "Which expression is not equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "a.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-y%29%282x%2By%29%284x%5E2+%2B+y%5E2%29 ALIGN=MIDDLE  ALT=\"%282x-y%29%282x%2By%29%284x%5E2+%2B+y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...expand<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+x%5E2+-+y%5E2%29%284x%5E2+%2B+y%5E2%29 ALIGN=MIDDLE  ALT=\"%284+x%5E2+-+y%5E2%29%284x%5E2+%2B+y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4%2B+4+x%5E2%2Ay%5E2++-+4x%5E2%2Ay%5E2+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4%2B+4+x%5E2%2Ay%5E2++-+4x%5E2%2Ay%5E2+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >->expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" >  equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E4+-+%28y%29%5E4 ALIGN=MIDDLE  ALT=\"%282x%29%5E4+-+%28y%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E4x%5E4%29+-+%28y%29%5E4 ALIGN=MIDDLE  ALT=\"%282%5E4x%5E4%29+-+%28y%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x%5E4%29+-+%28y%29%5E4 ALIGN=MIDDLE  ALT=\"%2816x%5E4%29+-+%28y%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >->expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" >  equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%284x%5E2+-+y%5E2%29+%2B+y%5E2%284x%5E2+-+y%5E2%29 ALIGN=MIDDLE  ALT=\"4x%5E2%284x%5E2+-+y%5E2%29+%2B+y%5E2%284x%5E2+-+y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+4x%5E2%2Ay%5E2%2B+4x%5E2+%2Ay%5E2+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4+-+4x%5E2%2Ay%5E2%2B+4x%5E2+%2Ay%5E2+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+cross%284x%5E2%2Ay%5E2%29%2B+cross%284x%5E2+%2Ay%5E2%29+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4+-+cross%284x%5E2%2Ay%5E2%29%2B+cross%284x%5E2+%2Ay%5E2%29+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4++-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4++-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >->expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" >  equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-y%29%288x%5E3+%2B+y%5E3%29 ALIGN=MIDDLE  ALT=\"%282x-y%29%288x%5E3+%2B+y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+8x%5E3%2A+y+%2B+2x%2A+y%5E3+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4+-+8x%5E3%2A+y+%2B+2x%2A+y%5E3+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >->expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+y%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4+-+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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