{"id":24439,"date":"2023-02-08T10:14:00","date_gmt":"2023-02-08T10:14:00","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24439"},"modified":"2023-02-08T18:27:37","modified_gmt":"2023-02-08T18:27:37","slug":"calcula-os-seguintes-produtos-e-somas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24439","title":{"rendered":"Calcula os seguintes produtos e somas"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24439' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24439' class='GTTabs_curr'><a  id=\"24439_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24439' ><a  id=\"24439_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_24439'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Nos mon\u00f3mios seguintes, as vari\u00e1veis designam-se por x, y e z.<\/p>\n<p>Calcula os seguintes produtos e somas de mon\u00f3mios e apresenta-os na forma can\u00f3nica.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 144px;\">\n<tbody>\n<tr style=\"height: 41px;\">\n<td style=\"width: 25%; height: 41px;\">\\(2{x^4} + 5{x^4}\\)<\/td>\n<td style=\"width: 25%; height: 41px;\">\\( &#8211; xy + 3xy\\)<\/td>\n<td style=\"width: 25%; height: 41px;\">\\(0,5xyz &#8211; \\frac{1}{2}xyz\\)<\/td>\n<td style=\"width: 25%; height: 41px;\">\\(\\frac{1}{2}{x^3} + 2{x^3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 41px;\">\n<td style=\"width: 25%; height: 41px;\">\\(\\frac{1}{2}{x^2}y &#8211; \\frac{5}{2}{x^2}y\\)<\/td>\n<td style=\"width: 25%; height: 41px;\">\\( &#8211; \\frac{3}{5}{x^2} + \\frac{2}{3}{x^2}\\)<\/td>\n<td style=\"width: 25%; height: 41px;\">\\(2yz + \\frac{5}{3}yz\\)<\/td>\n<td style=\"width: 25%; height: 41px;\">\\(x \\times 3{x^2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 25%; height: 62px;\">\\( &#8211; {x^2} \\times 0,5x\\)<\/td>\n<td style=\"width: 25%; height: 62px;\">\\(2x \\times 0,7xy\\)<\/td>\n<td style=\"width: 25%; height: 62px;\">\\( &#8211; \\frac{2}{7}{x^3} \\times \\left( { &#8211; \\frac{1}{5}{x^2}} \\right)\\)<\/td>\n<td style=\"width: 25%; height: 62px;\">\\(\\frac{1}{2}{x^3} \\times 2{x^5}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24439' onClick='GTTabs_show(1,24439)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24439'>\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><strong>a)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(2{x^4} + 5{x^4} = \\left( {2 + 5} \\right){x^4} = 7{x^4}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>b)<\/strong><\/td>\n<td style=\"text-align: left;\">\\( &#8211; xy + 3xy = \\left( { &#8211; 1 + 3} \\right)xy = 2xy\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>c)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(0,5xyz &#8211; \\frac{1}{2}xyz = \\left( {0,5 &#8211; \\frac{1}{2}} \\right)xyz = 0 \\times xyz = 0\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>d)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(\\frac{1}{2}{x^3} + 2{x^3} = \\left( {\\frac{1}{2} + 2} \\right){x^3} = \\left( {\\frac{1}{2} + \\frac{4}{2}} \\right){x^3} = \\frac{5}{2}{x^3}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>e)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(\\frac{1}{2}{x^2}y &#8211; \\frac{5}{2}{x^2}y = \\left( {\\frac{1}{2} &#8211; \\frac{5}{2}} \\right){x^2}y = &#8211; 2{x^2}y\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>f)<\/strong><\/td>\n<td style=\"text-align: left;\">\\( &#8211; \\frac{3}{{\\mathop 5\\limits_{\\left( 3 \\right)} }}{x^2} + \\frac{2}{{\\mathop 3\\limits_{\\left( 5 \\right)} }}{x^2} = \\left( { &#8211; \\frac{9}{{15}} + \\frac{{10}}{{15}}} \\right){x^2} = \\frac{1}{{15}}{x^2}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>g)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(2yz + \\frac{5}{3}yz = \\left( {\\frac{6}{3} + \\frac{5}{3}} \\right)yz = \\frac{{11}}{3}yz\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>h)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(x \\times 3{x^2} = \\left( {1 \\times 3} \\right) \\times \\left( {x \\times {x^2}} \\right) = 3{x^3}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>i)<\/strong><\/td>\n<td style=\"text-align: left;\">\\( &#8211; {x^2} \\times 0,5x = \\left( { &#8211; 1 \\times 0,5} \\right) \\times \\left( {{x^2} \\times x} \\right) = &#8211; 0,5{x^3}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>j)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(2x \\times 0,7xy = \\left( {2 \\times 0,7} \\right) \\times \\left( {x \\times xy} \\right) = 1,4{x^2}y\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>k)<\/strong><\/td>\n<td style=\"text-align: left;\">\\( &#8211; \\frac{2}{7}{x^3} \\times \\left( { &#8211; \\frac{1}{5}{x^2}} \\right) = \\left( { &#8211; \\frac{2}{7} \\times \\left( { &#8211; \\frac{1}{5}} \\right)} \\right) \\times \\left( {{x^3} \\times {x^2}} \\right) = \\frac{2}{{35}}{x^5}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>l)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(\\frac{1}{2}{x^3} \\times 2{x^5} = \\left( {\\frac{1}{2} \\times 2} \\right) \\times \\left( {{x^3} \\times {x^5}} \\right) = {x^8}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24439' onClick='GTTabs_show(0,24439)'>&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. Calcula os seguintes produtos e somas de mon\u00f3mios e apresenta-os na forma can\u00f3nica. \\(2{x^4} + 5{x^4}\\) \\( &#8211; xy +&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19269,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[100,97,700],"tags":[424,194,703,704],"series":[],"class_list":["post-24439","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","tag-operacoes-com-monomios"],"views":228,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat90.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24439","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=24439"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24439\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24439"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24439"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24439"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24439"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}