document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=125082>Question 125082</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have looked around and can not figure out how to solve these....this needs to be factored:\r<BR>\n" );
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document.write( "16x^4-81\r<BR>\n" );
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document.write( "Thanks in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91707 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=91707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve this problem you need to make use of the factor form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2+-+B%5E2+=+%28A+-+B%29%28A+%2B+B%29 ALIGN=MIDDLE  ALT=\"A%5E2+-+B%5E2+=+%28A+-+B%29%28A+%2B+B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which says that the difference between two squares is equal to the product of two binomials that<BR>\n" );
document.write( "are formed by the difference and the sum of the square roots of the two squares.<BR>\n" );
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document.write( "Suppose you let A represent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2%29 ALIGN=MIDDLE  ALT=\"%284x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Then A^2 would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2%29%5E2%29 ALIGN=MIDDLE  ALT=\"%284x%5E2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this is equal<BR>\n" );
document.write( "to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4 ALIGN=MIDDLE  ALT=\"16x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In addition we can say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81+=+9%5E2 ALIGN=MIDDLE  ALT=\"81+=+9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "If we substitute those two values into the factor form we get the difference of two squares<BR>\n" );
document.write( "on the left side, so the factored form is the right side and it consists of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2%29%5E2+-+9%5E2+=+%284x%5E2+-+9%29%284x%5E2+%2B+9%29 ALIGN=MIDDLE  ALT=\"%284x%5E2%29%5E2+-+9%5E2+=+%284x%5E2+-+9%29%284x%5E2+%2B+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then notice that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-9 ALIGN=MIDDLE  ALT=\"4x%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > also fits the factor form because it can be written as<BR>\n" );
document.write( "the difference of two squares in the factor form as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E2+-+3%5E2+=+%282x+-+3%29%282x+%2B+3%29 ALIGN=MIDDLE  ALT=\"%282x%29%5E2+-+3%5E2+=+%282x+-+3%29%282x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute this factored form for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2+-+9%29 ALIGN=MIDDLE  ALT=\"%284x%5E2+-+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the whole thread of factoring<BR>\n" );
document.write( "results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E4+-+81+=+%284x%5E2%29%5E2+-+9%5E2+=+%282x+-+3%29%282x+%2B+3%29%284x%5E2+%2B+9%29 ALIGN=MIDDLE  ALT=\"16x%5E4+-+81+=+%284x%5E2%29%5E2+-+9%5E2+=+%282x+-+3%29%282x+%2B+3%29%284x%5E2+%2B+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And that is the answer to your problem. Hope that you can track this OK. It's a little bit<BR>\n" );
document.write( "difficult to explain.<BR>\n" );
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