43

<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>43</B></div> <div> <B>M u l t i p l i c a c i ó n </B></div> <div> <B>Multiplicación de polinomios por polinomios</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> <div> autos, bebidas, bancos, automóviles, celulares, seguros, arrendamientos, poliza de seguro, aviones, vacaciones, hoteles, </div> <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 ordenan los polinomios</FONT></div> <div> <B>2.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se escriben el multiplicando y el multiplicador en dos filas: el multiplicando en la fila superior y el multiplicador en la inferior. Se traza una linea horizontal debajo de estas dos filas</FONT></div> <div> <FONT SIZE="4" COLOR="#FF9900" FACE="Bell MT" ><B>3.</B></FONT>  Se multiplica cada termino del multiplicador por todos los terminos del multiplicando (teniendo en cuenta la <I>ley de los signos</I> y <I>la ley de los exponentes)</I></div> <div> <B>4.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Cada producto particular se escribe en su respectiva fila debajo de la linea horizontal y en el orden en que se efectuaron los productos parciales: en la primera fila, el producto del primer termino del multiplicador y todos los del mutiplicando; en la segunda fila, el producto del segundo termino del multiplicador y todos los del mutiplicando; en la tercera fila, el producto del tercer termino del multiplicador y todos los del mutiplicando; ...</FONT></div> <div> <B>5.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Los términos smejantes se escriben en la misma columna</FONT></div> <div> <B>6.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se reducen los términos semejantes</FONT></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="7" CELLSPACING="1" WIDTH="844" BORDERCOLORLIGHT="#FFCC66" BORDERCOLORDARK="#990000" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 123 WIDTH="361"><div> <B>Ley de los signos</B></div> <div> +  por  +  da  +</div> <div> +  por  -  da  -</div> <div> -   por  +  da  -</div> <div> -  por  -  da  +</div> </tD> <tD VALIGN=TOP WIDTH="446"><div> <B>Propiedad en el producto de potencias</B></div> <div> Para hallar el producto de dos o más potencias con la misma base, basta con escribir la base común y sumar los exponentes respectivos.</div> </tD> </tR> </TABLE></div> <bR> <div> <B>Enunciados de los ejercicios</B></div> <bR> <div> <B> </B><FONT SIZE="4" COLOR="#00CC00" FACE="Bell MT" ><B>M</B></FONT><FONT SIZE="4" COLOR="#339933" FACE="Bell MT" ><B> </B></FONT><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >u l t i l p l i c a r :</FONT></div> <bR> <div> <IMG SRC="6efce51b0.gif" border=0 width="229" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#1" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/KSEvCtcnZvM?t=22s" TARGET="_top" TITLE="https://youtu.be/KSEvCtcnZvM?t=22s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="6efd041b0.gif" border=0 width="260" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#2" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/KSEvCtcnZvM?t=5m39s" TARGET="_top" TITLE="https://youtu.be/KSEvCtcnZvM?t=5m39s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="6efe551b0.gif" border=0 width="341" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#3" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/KSEvCtcnZvM?t=11m6s" TARGET="_top" TITLE="https://youtu.be/KSEvCtcnZvM?t=11m6s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>        <IMG SRC="6eff171b0.gif" border=0 width="279" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#4" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/G7Aaydya3FY" TARGET="_top" TITLE="https://youtu.be/G7Aaydya3FY"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>    <IMG SRC="6f00201b0.gif" border=0 width="288" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#5" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/lE991f4jUfQ" TARGET="_top" TITLE="https://youtu.be/lE991f4jUfQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>        <IMG SRC="6f01251b0.gif" border=0 width="293" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#6" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/yHJwwQ6XuQo" TARGET="_top" TITLE="https://youtu.be/yHJwwQ6XuQo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>   <IMG SRC="6f02451b0.gif" border=0 width="325" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#7" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/Qea4U1NLqM0" TARGET="_top" TITLE="https://youtu.be/Qea4U1NLqM0"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="6f03a01b0.gif" border=0 width="416" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#8" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/THLSwFdjSeI" TARGET="_top" TITLE="https://youtu.be/THLSwFdjSeI"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>    <IMG SRC="6f04931b0.gif" border=0 width="403" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#9" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/p8DN1kJzbqg" TARGET="_top" TITLE="https://youtu.be/p8DN1kJzbqg"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>        <IMG SRC="6f05a11b0.gif" border=0 width="417" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#10" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/n3pDanaBBjc" TARGET="_top" TITLE="https://youtu.be/n3pDanaBBjc"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>     <IMG SRC="6f06cd1b0.gif" border=0 width="205" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#11" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/Vehlm90a_h4" TARGET="_top" TITLE="https://youtu.be/Vehlm90a_h4"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="6f07cd1b0.gif" border=0 width="205" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#12" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/mFZgmxMQ41k" TARGET="_top" TITLE="https://youtu.be/mFZgmxMQ41k"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> </div> <div> <IMG SRC="6f08a41b0.gif" border=0 width="420" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#13" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/OWvvQ_hTBrU?t=21s" TARGET="_top" TITLE="https://youtu.be/OWvvQ_hTBrU?t=21s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> </div> <div> <IMG SRC="6f09411b0.gif" border=0 width="577" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#14" TITLE="43"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <A HREF="https://youtu.be/OWvvQ_hTBrU?t=9m42s" TARGET="_top" TITLE="https://youtu.be/OWvvQ_hTBrU?t=9m42s"><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 rerproducción sobre la solución del Ejercicio 43</B></div> <bR> <div> <B> <iframe width="853" height="480" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo1qjYD52ZpZebQnYTt5jrVD" frameborder="0" allowfullscreen></iframe>  </B></div> <bR> <div> <B>M </B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >u l t i p l i c a r :</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="5aad44fc0.gif" border=0 width="324" height="252" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <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="5b06d8fd0.gif" border=0 width="472" height="253" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <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="5b07bf190.gif" border=0 width="703" height="281" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <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="5b0563fd0.gif" border=0 width="611" height="253" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <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="5b08a0fd0.gif" border=0 width="672" height="253" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <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="5b0974190.gif" border=0 width="628" height="281" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <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="5b0a9d190.gif" border=0 width="669" height="281" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>8</div> <div> <IMG SRC="5aae33190.gif" border=0 width="819" height="281" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>9</div> <div> <IMG SRC="5b0bc7190.gif" border=0 width="711" height="281" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>10</div> <div> <IMG SRC="5b0c08fd0.gif" border=0 width="776" height="253" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>11</div> <div> <IMG SRC="5b0e5bd90.gif" border=0 width="347" height="217" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>12</div> <div> <IMG SRC="5aaf47fc0.gif" border=0 width="583" height="252" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>13</div> <div> <IMG SRC="5b0d00190.gif" border=0 width="768" height="281" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="14"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>14</div> <div> <IMG SRC="5ab0803b0.gif" border=0 width="896" height="315" ALT="MathType 5.0 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" 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