{"id":6898,"date":"2011-06-06T22:38:13","date_gmt":"2011-06-06T21:38:13","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6898"},"modified":"2022-01-05T15:44:08","modified_gmt":"2022-01-05T15:44:08","slug":"transforma-as-seguintes-expressoes-em-produtos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6898","title":{"rendered":"Transforma as seguintes express\u00f5es em produtos"},"content":{"rendered":"<p><ul id='GTTabs_ul_6898' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6898' class='GTTabs_curr'><a  id=\"6898_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6898' ><a  id=\"6898_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_6898'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Transforma as seguintes express\u00f5es em produtos, colocando os fatores comuns em evid\u00eancia:<\/p>\n<ol>\n<li>$mx+nx$<\/li>\n<li>$6+3x$<\/li>\n<li>$4a-8$<\/li>\n<li>$5x-10{{x}^{2}}$<\/li>\n<li>$8{{x}^{2}}+2x-4$<\/li>\n<li>$5{{a}^{3}}-15{{a}^{2}}+5a$<\/li>\n<li>$\\frac{1}{5}{{x}^{3}}-3{{x}^{2}}$<\/li>\n<li>$3(x-5)+x(x-5)$<\/li>\n<li>$\\frac{1}{2}(x-2)+(x-2)x$<\/li>\n<li>${{(x+7)}^{2}}-(x+7)$<\/li>\n<li>${{(x-2)}^{2}}-2(x-2)$<\/li>\n<li>$6+2y+3x+xy$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6898' onClick='GTTabs_show(1,6898)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6898'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$mx+nx=x(m+n)$<\/li>\n<li>Ora,<br \/>\n$6+3x=3(2+x)$<\/li>\n<li>Ora,<br \/>\n$4a-8=4(a-2)$<\/li>\n<li>Ora,<br \/>\n$5x-10{{x}^{2}}=5x(1-2x)$<\/li>\n<li>Ora,<br \/>\n$8{{x}^{2}}+2x-4=2(4{{x}^{2}}+x-2)$<\/li>\n<li>Ora,<br \/>\n$5{{a}^{3}}-15{{a}^{2}}+5a=5a({{a}^{2}}-3a+1)$<\/li>\n<li>Ora,<br \/>\n$\\frac{1}{5}{{x}^{3}}-3{{x}^{2}}={{x}^{2}}(\\frac{1}{5}x-3)$<\/li>\n<li>Ora,<br \/>\n$3(x-5)+x(x-5)=(x-5)(3+x)$<\/li>\n<li>Ora,<br \/>\n$\\frac{1}{2}(x-2)+(x-2)x=(x-2)(\\frac{1}{2}+x)$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n{{(x+7)}^{2}}-(x+7) &amp; = &amp; (x+7)\\left[ (x+7)-1 \\right]\u00a0 \\\\<br \/>\n{} &amp; = &amp; (x+7)(x+6)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n{{(x-2)}^{2}}-2(x-2) &amp; = &amp; (x-2)\\left[ (x-2)-2 \\right]\u00a0 \\\\<br \/>\n{} &amp; = &amp; (x-2)(x-4)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n6+2y+3x+xy &amp; = &amp; 2(3+y)+x(3+y)\u00a0 \\\\<br \/>\n{} &amp; = &amp; (2+x)(3+y)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6898' onClick='GTTabs_show(0,6898)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Transforma as seguintes express\u00f5es em produtos, colocando os fatores comuns em evid\u00eancia: $mx+nx$ $6+3x$ $4a-8$ $5x-10{{x}^{2}}$ $8{{x}^{2}}+2x-4$ $5{{a}^{3}}-15{{a}^{2}}+5a$ $\\frac{1}{5}{{x}^{3}}-3{{x}^{2}}$ $3(x-5)+x(x-5)$ $\\frac{1}{2}(x-2)+(x-2)x$ ${{(x+7)}^{2}}-(x+7)$ ${{(x-2)}^{2}}-2(x-2)$ $6+2y+3x+xy$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19189,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,193],"tags":[197],"series":[],"class_list":["post-6898","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-de-grau-superior-ao-1-","tag-decomposicao-em-factores"],"views":1950,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat75.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6898","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=6898"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6898\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19189"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6898"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6898"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6898"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}