document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=494627>Question 494627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a hard time with multiplying out (2+h)^3. I have tried to do <BR>\n" );
document.write( "(2+h)(2+h)(2+h) and did (2^2+2h+h^2)=  (4+2h+h^2) . I am using this in Derivatives. \r<BR>\n" );
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document.write( "So If f(x)=x^3 I have to find the tangent line of the equation through point (2,8). \r<BR>\n" );
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document.write( "So F'(2+h)= ((2+h))^3 Which is (4+2h+h^2)<BR>\n" );
document.write( "Then F'(2)= (2)^3 Which is (8)\r<BR>\n" );
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document.write( "So then I take (4+2h+h^2)-(8)\r<BR>\n" );
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document.write( "and I get -4+2h+h^2/h Do you see my problem.\r<BR>\n" );
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document.write( "I have tried this so many different ways. Where am I making my error? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335730 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=335730\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You should definitely review how to multiply polynomials before pursuing a calculus course. To multiply out (2+h)^3, use the binomial theorem and expand.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (2+h)^3 = (3C0)2^3 + (3C1)2^2h + (3C2)2h^2 + (3C3)h^3\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = 8 + 12h + 6h^2 + h^3\">\r<BR>\n" );
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document.write( "This is assuming you want to evaluate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\"> where x=2.\r<BR>\n" );
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document.write( "Or, if you know that the derivative of x^3 is 3x^2, we can easily find the tangent line.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f'(x) = 3x^2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f'(2) = 3(2)^2 = 12\">\r<BR>\n" );
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document.write( "Hence we can write the tangent line in point-slope form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y-8 = 12(x-2)\"> </SPAN>\n" );
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