66

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#003333" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Álgebra de Baldor"><U><B>Algebra de Baldor</B></U></A><B> |  </B><A HREF="id1076.htm" TARGET="_top" TITLE="Índice temático"><U><B>Índice temático</B></U></A><B>  |  </B><A HREF="id1073.htm" TARGET="_top" TITLE="Lista"><U><B>Lista de Ejercicios</B></U></A><B> |</B></div> <bR> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>66</B></div> <div> <B>P r o d u c t o s   y   c o c i e n t e s   n o t a b l e s</B></div> <div> <B>Productos notables</B></div> <div> <B>Cubo de un binomio</B></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B>P r o c e d i m i e n t o</B> :</div> <div> <B>1.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se desarrolla el paréntesis, observando si se trata del cubo, de la suma o la diferencia de dos cantidades; en el primer caso se procede como indica el paso </FONT>2<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >, en el segundo caso se aplica el enunciado del paso </FONT>3<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >:</FONT><B> </B></div> <div> <B>2.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  "El cubo de la suma de dos cantidades es igual al cubo de la primera cantidad más el triplo del cuadrado de la primera por la segunda, más el triplo de la primera por el cuadrado de la segunda, más el cubo de la segunda"</FONT></div> <div> <B>3.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  "El cubo de la diferencia de dos cantidades es igual al cubo de la primera cantidad menos el triplo del cuadrado de la primera por la segunda, más el triplo de la primera por el cuadrado de la segunda, menos el cubo de la segunda"</FONT></div> <div> <B>4.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se efectúan las operaciones que quedan indicadas.</FONT></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="73f20b1d0.gif" border=0 width="267" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <B>Enunciados de los problemas del Ejercicio 66</B></div> <bR> <div> <B>          S</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >olución en imagen <IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> y o video <IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> de los doce problemas del Ejercicio 66:</FONT></div> <div> <B>D</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >esarollar:</FONT></div> <div> <FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="73e7551b0.gif" border=0 width="85" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#1" TITLE="66"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/r9KHQ7ZFN8s" TARGET="_top" TITLE="https://youtu.be/r9KHQ7ZFN8s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="73d9531b0.gif" border=0 width="83" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#2" TITLE="66"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/r9KHQ7ZFN8s?t=7m43s" TARGET="_top" TITLE="https://youtu.be/r9KHQ7ZFN8s?t=7m43s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="73e8591b0.gif" border=0 width="89" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#3" TITLE="66"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/r9KHQ7ZFN8s?t=9m28s" TARGET="_top" TITLE="https://youtu.be/r9KHQ7ZFN8s?t=9m28s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" ><IMG SRC="73e9571b0.gif" border=0 width="87" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#4" TITLE="66"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/X6vj2-34LVA" TARGET="_top" TITLE="https://youtu.be/X6vj2-34LVA"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="73ea5c1b0.gif" border=0 width="92" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#5" TITLE="66"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/X6vj2-34LVA?t=8m29s" TARGET="_top" TITLE="https://youtu.be/X6vj2-34LVA?t=8m29s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >       <IMG SRC="73eb5c1b0.gif" border=0 width="92" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#6" TITLE="66"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/--mMDHvh6Go" TARGET="_top" TITLE="https://youtu.be/--mMDHvh6Go"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="73ec601b0.gif" border=0 width="96" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#7" TITLE="66"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/--mMDHvh6Go?t=9m33s" TARGET="_top" TITLE="https://youtu.be/--mMDHvh6Go?t=9m33s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="73ed5c1b0.gif" border=0 width="92" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/tMjlVH7fmLY" TARGET="_top" TITLE="https://youtu.be/tMjlVH7fmLY"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="73ee5f1b0.gif" border=0 width="95" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/Rg7AVH4rHIY" TARGET="_top" TITLE="https://youtu.be/Rg7AVH4rHIY"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="73ef731b0.gif" border=0 width="115" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/EBvpkng-qLg" TARGET="_top" TITLE="https://youtu.be/EBvpkng-qLg"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>      <IMG SRC="73f0741b0.gif" border=0 width="116" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/CPBP5A65YzY" TARGET="_top" TITLE="https://youtu.be/CPBP5A65YzY"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="73f1651b0.gif" border=0 width="101" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/gpqs5Y6V42M" TARGET="_top" TITLE="https://youtu.be/gpqs5Y6V42M"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT> </div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Lista de reproducción sobre las soluciones del Ejercicio 66</B></div> <bR> <div> <B> <iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo1cD20l99k5lMMvqIBt5v0U" frameborder="0" allowfullscreen></iframe>  </B></div> <div> <B>D</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >esarollar:</FONT></div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <IMG SRC="5bdff36f0.gif" border=0 width="499" height="111" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <IMG SRC="5be4286f0.gif" border=0 width="296" height="111" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <IMG SRC="5be5136f0.gif" border=0 width="531" height="111" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <IMG SRC="5be6046f0.gif" border=0 width="516" height="111" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <IMG SRC="5be0376f0.gif" border=0 width="567" height="111" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="5be76c6f0.gif" border=0 width="620" height="111" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>7</div> <div> <IMG SRC="5be8686f0.gif" border=0 width="616" height="111" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <DIV ALIGN="LEFT"></DIV> <div> <A HREF="http://twitter.com/Calculo21" TARGET="_top" TITLE="http://twitter.com/Calculo21"><U><IMG SRC="2fc828280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="http://www.facebook.com/juan.beltran.58511" TARGET="_top" TITLE="http://www.facebook.com/juan.beltran.585"><U><IMG SRC="76fa28280.gif" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A 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