47

<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> <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>47</B></div> <div> <B>M u l t i p l i c a c i ó n </B></div> <div> <B>Multiplicación combinada con suma y resta</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> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="177" BORDERCOLORLIGHT="#FFCC66" BORDERCOLORDARK="#990000" FRAME="BOX" RULES="ALL" ALIGN="RIGHT" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 123 ><NOBR><div> <B>Ley de los signos</B></div> <div> +  por  +  da  +</div> <div> +  por  -  da  -</div> <div> -   por  +  da  -</div> <div> -  por  -  da  +</div> </NOBR></tD> </tR> </TABLE></div> <div> <FONT SIZE="4" COLOR="#FF9900" FACE="Bell MT" ><B>1.</B></FONT>  Se efectúan los productos indicados: multiplicando cada término del multiplicador por cada uno de los terminos del multiplicando (teniendo en cuenta la <I>ley de los signos</I> y la<I> ley de los exponentes)</I></div> <div> <B>2.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se reducen los términos semejantes</FONT></div> <div> <B>Nota1:</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > Deducción de la fórmula general para el "</FONT>cuadrado de un binomio<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >":</FONT></div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="6f5db4390.gif" border=0 width="436" height="57" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0">  </div> <div> <B>Nota2:</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > Deducción de la fórmula general para el "producto de la suma por la diferencia de dos cantidades":</FONT></div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="5ad614180.gif" border=0 width="276" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <B>Enunciados de los ejercicios</B></div> <bR> <bR> <div> <B>S</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > i m p l i f i c a r :</FONT></div> <div> <IMG SRC="6f5ea5190.gif" border=0 width="165" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#1" TITLE="47"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/4olr_lnEL2A" TARGET="_top" TITLE="https://youtu.be/4olr_lnEL2A"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="6f5f051c0.gif" border=0 width="261" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#2" TITLE="47"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/-LlyeCJDpFc" TARGET="_top" TITLE="https://youtu.be/-LlyeCJDpFc"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="6f6011190.gif" border=0 width="273" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#3" TITLE="47"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/iNNDNa7yLlo" TARGET="_top" TITLE="https://youtu.be/iNNDNa7yLlo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="6f660d1f0.gif" border=0 width="269" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/WnUF7cYnSTs" TARGET="_top" TITLE="https://youtu.be/WnUF7cYnSTs"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="6f676d1f0.gif" border=0 width="365" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/03yneji9JhY" TARGET="_top" TITLE="https://youtu.be/03yneji9JhY"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="6f682b1f0.gif" border=0 width="299" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/wnn4CReVD3Y" TARGET="_top" TITLE="https://youtu.be/wnn4CReVD3Y"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="6f69fc1c0.gif" border=0 width="252" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/hzQgVFLMJWE" TARGET="_top" TITLE="https://youtu.be/hzQgVFLMJWE"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      </div> <div> <IMG SRC="6f6a601c0.gif" border=0 width="352" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/Pcp0bkqcDm0" TARGET="_top" TITLE="https://youtu.be/Pcp0bkqcDm0"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="6f6bc01c0.gif" border=0 width="448" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/yCzhWsQ1kxw" TARGET="_top" TITLE="https://youtu.be/yCzhWsQ1kxw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="6f6cb5200.gif" border=0 width="181" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/X0ZKr1V-RME" TARGET="_top" TITLE="https://youtu.be/X0ZKr1V-RME"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="6f6d29200.gif" border=0 width="297" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/KM1NtidgBjI" TARGET="_top" TITLE="https://youtu.be/KM1NtidgBjI"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="6f6e25200.gif" border=0 width="293" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/ylN5yueMeJ8" TARGET="_top" TITLE="https://youtu.be/ylN5yueMeJ8"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="6f6f90200.gif" border=0 width="400" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/2V6kSIkQXBQ" TARGET="_top" TITLE="https://youtu.be/2V6kSIkQXBQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="6f7055200.gif" border=0 width="341" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/Ovbfu355r74" TARGET="_top" TITLE="https://youtu.be/Ovbfu355r74"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="6f7170210.gif" border=0 width="368" height="33" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/rC1r8epeaQo" TARGET="_top" TITLE="https://youtu.be/rC1r8epeaQo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>     <IMG SRC="6f728d210.gif" border=0 width="397" height="33" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/Cxj4glXXRb8" TARGET="_top" TITLE="https://youtu.be/Cxj4glXXRb8"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="6f73451f0.gif" border=0 width="325" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/tlLQmxXdoGw" TARGET="_top" TITLE="https://youtu.be/tlLQmxXdoGw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="6f614f190.gif" border=0 width="335" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#18" TITLE="47"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/hJMC4Cil0-w" TARGET="_top" TITLE="https://youtu.be/hJMC4Cil0-w"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="6f62c0190.gif" border=0 width="448" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#19" TITLE="47"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/SzF3STUuE7g" TARGET="_top" TITLE="https://youtu.be/SzF3STUuE7g"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="6f638b1c0.gif" border=0 width="395" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#20" TITLE="47"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/G9_0QlK8vxU" TARGET="_top" TITLE="https://youtu.be/G9_0QlK8vxU"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Lista de reproducción sobre las soluciones del Ejercicio 47</B></div> <bR> <div> <B> <iframe width="853" height="480" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo3DcbJR0hdAWgZQjLHsNCdv" frameborder="0" allowfullscreen></iframe>  </B></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="5ac1d56c0.gif" border=0 width="725" height="108" 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="5ad980740.gif" border=0 width="896" height="116" 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="5adae18c0.gif" border=0 width="737" height="140" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="18"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>18</div> <div> <IMG SRC="5ac241e10.gif" border=0 width="833" height="225" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="19"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>19</div> <div> <IMG SRC="5adb50040.gif" border=0 width="848" height="260" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="20"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>20</div> <div> <IMG SRC="5adc41240.gif" border=0 width="833" height="292" 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 HREF="https://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="https://www.youtube.com/user/MatematicaA"><U><IMG SRC="2fca28280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <div> Por: <FONT SIZE="4" COLOR="#FF9900" FACE="Times New Roman" >Juan Carlos </FONT><FONT SIZE="4" COLOR="#0000FF" FACE="Times New Roman" >Beltrán</FONT> <FONT SIZE="4" COLOR="#FF0000" FACE="Times New Roman" >Beltrán </FONT></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 = 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