{"id":24430,"date":"2023-02-07T22:37:19","date_gmt":"2023-02-07T22:37:19","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24430"},"modified":"2023-02-07T23:14:03","modified_gmt":"2023-02-07T23:14:03","slug":"escreve-na-forma-canonica-o-produto-dos-monomios","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24430","title":{"rendered":"Escreve, na forma can\u00f3nica, o produto dos mon\u00f3mios"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24430' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24430' class='GTTabs_curr'><a  id=\"24430_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24430' ><a  id=\"24430_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_24430'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Nos mon\u00f3mios seguintes, as vari\u00e1veis designam-se por <em>x<\/em>, <em>y<\/em> e z e as constantes por <em>a<\/em>, <em>b<\/em> e <em>c<\/em>.<\/p>\n<p>Escreve, na forma can\u00f3nica, o produto dos seguintes mon\u00f3mios e, caso os mon\u00f3mios sejam semelhantes, determina igualmente a respetiva soma.<\/p>\n<ol>\n<li>\\(3{x^2}\\) e \\(7{x^3}\\)<\/li>\n<li>\\(2y\\) e \\(5ay\\)<\/li>\n<li>\\(4{x^2}y\\) e \\(8y{x^2}\\)<\/li>\n<li>\\(12abc{x^2}{y^3}{z^4}\\) e \\(3b{a^2}xyz\\)<\/li>\n<li>\\(\\left( {3 + 2b} \\right){x^2}\\) e \\(7axy\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24430' onClick='GTTabs_show(1,24430)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24430'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td colspan=\"2\"><strong>Mon\u00f3mios<\/strong><\/td>\n<td><strong>Produto<\/strong><\/td>\n<td><strong>Soma<\/strong><\/td>\n<\/tr>\n<tr>\n<td>1.<\/td>\n<td>\\(3{x^2}\\)<\/td>\n<td>\\(7{x^3}\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">\\(3{x^2} \\times 7{x^3} = \\left( {3 \\times 7} \\right) \\times \\left( {{x^2} \\times {x^3}} \\right) = 21{x^5}\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">Os mon\u00f3mios n\u00e3o s\u00e3o semelhantes.<\/td>\n<\/tr>\n<tr>\n<td>2.<\/td>\n<td>\\(2y\\)<\/td>\n<td>\\(5ay\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">\\(2y \\times 5ay = \\left( {2 \\times 5a} \\right) \\times \\left( {y \\times y} \\right) = 10a{y^2}\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">\\(2y + 5ay = \\left( {2 + 5a} \\right)y\\)<\/td>\n<\/tr>\n<tr>\n<td>3.<\/td>\n<td>\\(4{x^2}y\\)<\/td>\n<td>\\(8y{x^2}\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">\\(4{x^2}y \\times 8y{x^2} = \\left( {4 \\times 8} \\right) \\times \\left( {{x^2}y \\times y{x^2}} \\right) = 32{x^4}{y^2}\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">\\(4{x^2}y + 8y{x^2} = \\left( {4 + 8} \\right) \\times {x^2}y = 12{x^2}y\\)<\/td>\n<\/tr>\n<tr>\n<td>4.<\/td>\n<td>\\(12abc{x^2}{y^3}{z^4}\\)<\/td>\n<td>\\(3b{a^2}xyz\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">\\(12abc{x^2}{y^3}{z^4} \\times 3b{a^2}xyz = 36{a^3}{b^2}c{x^3}{y^4}{z^5}\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">Os mon\u00f3mios n\u00e3o s\u00e3o semelhantes.<\/td>\n<\/tr>\n<tr>\n<td>5.<\/td>\n<td>\\(\\left( {3 + 2b} \\right){x^2}\\)<\/td>\n<td>\\(7axy\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">\\(\\left( {3 + 2b} \\right){x^2} \\times 7axy = 7a\\left( {3 + 2b} \\right){x^3}y\\)<\/td>\n<td style=\"text-align: left; vertical-align: top;\">Os mon\u00f3mios n\u00e3o s\u00e3o semelhantes.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24430' onClick='GTTabs_show(0,24430)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Nos mon\u00f3mios seguintes, as vari\u00e1veis designam-se por x, y e z e as constantes por a, b e c. Escreve, na forma can\u00f3nica, o produto dos seguintes mon\u00f3mios e, caso os&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,194,703],"series":[],"class_list":["post-24430","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-monomios-e-polinomios","tag-8-o-ano","tag-monomios","tag-monomios-semelhantes"],"views":988,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat56.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24430","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=24430"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24430\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24430"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24430"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24430"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24430"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}