{"id":2163,"date":"2019-09-18T17:33:01","date_gmt":"2019-09-18T17:33:01","guid":{"rendered":"http:\/\/lash.utrng.edu.mx\/?p=2163"},"modified":"2020-05-13T22:18:37","modified_gmt":"2020-05-13T22:18:37","slug":"productos-notables","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=2163","title":{"rendered":"Productos notables"},"content":{"rendered":"\n<p>Se le llama <strong>Productos notables<\/strong> a aquellas multiplicaciones que cumplen reglas fijas y cuyo resultado <strong>puede ser dado por simple inspecci\u00f3n<\/strong>, es decir, sin verificaci\u00f3n.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-notable01.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"278\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-notable01-1024x278.jpg\" alt=\"\" class=\"wp-image-2164\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-notable01-1024x278.jpg 1024w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-notable01-300x82.jpg 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-notable01-768x209.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<!--more-->\n\n\n\n<p>Vemos que, <strong>El cuadrado de la suma de dos cantidades es igual al cuadrado de la primera cantidad m\u00e1s el doble de la primera cantidad por la segunda, m\u00e1s el cuadrado de la segunda cantidad.<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-luminous-vivid-orange-color\"><strong>Ejemplo<\/strong>:<\/p>\n\n\n\n<p>Desarrollar (X+4)<sup> 2 <\/sup><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>Cuadrado del primero<\/td><td>X<sup>2<\/sup><\/td><\/tr><tr><td>Doble del primero por el segundo<\/td><td>2X x 4 = 8X<\/td><\/tr><tr><td>Cuadrado del segundo<\/td><td>16<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center\">tenemos entonces que <strong>(X+4)<\/strong><sup><strong> 2 <\/strong><\/sup><strong> = X<\/strong><sup><strong>2<\/strong><\/sup><strong> + 8X + 16<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator is-style-dots\"\/>\n\n\n\n<p class=\"has-text-color has-vivid-red-color\"><strong>Cuadrado de un monomio<\/strong><\/p>\n\n\n\n<p>Para elevar un monomio al cuadrado, se eleva su <strong>coeficiente <\/strong>al cuadrado y se multiplica por 2 cada exponente de sus letras. P. ej.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>(4ab<\/strong><sup><strong>2<\/strong><\/sup><strong>)<\/strong><sup><strong>2<\/strong><\/sup><strong> = 4<\/strong><sup><strong>2<\/strong><\/sup><strong>a<\/strong><sup><strong>1&#215;2<\/strong><\/sup><strong>b<\/strong><sup><strong>2&#215;2<\/strong><\/sup><strong>= 16a<\/strong><sup><strong>2<\/strong><\/sup><strong>b<\/strong><sup><strong>4<\/strong><\/sup><\/p>\n\n\n\n<hr class=\"wp-block-separator is-style-dots\"\/>\n\n\n\n<p class=\"has-text-color has-vivid-cyan-blue-color\"><strong>Ejemplo:<\/strong><\/p>\n\n\n\n<p>(3a<sup>2<\/sup> + 5x<sup>3<\/sup>)<sup>2<\/sup><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>Cuadrado del primero<\/td><td>9a<sup>4<\/sup><\/td><\/tr><tr><td>Doble del primero por el segundo<\/td><td>2(3a<sup>2<\/sup> + 5x<sup>3<\/sup>) = <br>2  (15a<sup>2<\/sup> x<sup>3<\/sup>)  = 30a<sup>2<\/sup> x<sup>3<\/sup><\/td><\/tr><tr><td>Cuadrado del segundo<\/td><td>25x<sup>6<\/sup><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Tenemos entonces que, <strong>(3a<\/strong><sup><strong>2<\/strong><\/sup><strong> + 5x<\/strong><sup><strong>3<\/strong><\/sup><strong>)<\/strong><sup><strong>2<\/strong><\/sup><strong> = 9a<\/strong><sup><strong>4<\/strong><\/sup><strong> + 30a<\/strong><sup><strong>2<\/strong><\/sup><strong> x<\/strong><sup><strong>3<\/strong><\/sup><strong> + 25x<\/strong><sup><strong>6<\/strong><\/sup><\/p>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-background has-medium-font-size has-very-light-gray-color has-vivid-red-background-color\"><strong>Ejercicios<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-Notables-ejercicios.jpg\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"210\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-Notables-ejercicios-1024x210.jpg\" alt=\"\" class=\"wp-image-2165\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-Notables-ejercicios-1024x210.jpg 1024w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-Notables-ejercicios-300x62.jpg 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/09\/Prod-Notables-ejercicios-768x158.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Se le llama Productos notables a aquellas multiplicaciones que cumplen reglas fijas y cuyo resultado puede ser dado por simple inspecci\u00f3n, es decir, sin verificaci\u00f3n.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[28,60],"tags":[],"class_list":["post-2163","post","type-post","status-publish","format-standard","hentry","category-primerparcialmate","category-primerparcialmate-textil"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2163","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2163"}],"version-history":[{"count":3,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2163\/revisions"}],"predecessor-version":[{"id":2592,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2163\/revisions\/2592"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2163"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2163"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2163"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}