{"id":347,"date":"2023-07-06T02:26:23","date_gmt":"2023-07-06T02:26:23","guid":{"rendered":"https:\/\/mathority.org\/it\/trinomio-quadrato\/"},"modified":"2023-07-06T02:26:23","modified_gmt":"2023-07-06T02:26:23","slug":"trinomio-quadrato","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/trinomio-quadrato\/","title":{"rendered":"Trinomio quadrato"},"content":{"rendered":"<p>In questa pagina spieghiamo come risolvere il quadrato di un trinomio (formula). Inoltre, potrai vedere diversi esempi ed esercitarti con esercizi risolti passo dopo passo di trinomi quadrati. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-un-trinomio-al-cuadrado\"><\/span> Formula per un trinomio quadrato<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Logicamente, per comprendere la formula del trinomio al quadrato, devi prima sapere cos&#8217;\u00e8 un <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/trinomio\/\">trinomio<\/a><\/span><\/strong> . Ti lascio questo link nel caso volessi rivederlo prima di proseguire con la spiegazione.<\/p>\n<p> Un <strong>trinomio al quadrato<\/strong> \u00e8 uguale al quadrato del primo termine, pi\u00f9 il quadrato del secondo termine, pi\u00f9 il quadrato del terzo termine, pi\u00f9 il doppio del primo termine per il secondo, pi\u00f9 il doppio del primo termine per il terzo, pi\u00f9 il doppio del secondo per il terzo. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/carre-dun-trinome.png\" alt=\"quadrato di un trinomio o trinomio al quadrato\" class=\"wp-image-2847\" width=\"378\" height=\"302\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Il quadrato di un trinomio \u00e8 cos\u00ec importante perch\u00e9 \u00e8 un prodotto notevole (o identit\u00e0 notevole), cio\u00e8 esiste una formula matematica che permette di calcolare rapidamente questa operazione. Fare clic sul seguente collegamento per vedere quali sono tutte le<a href=\"https:\/\/mathority.org\/it\/identita-prodotti-uguaglianze-notevoli-esercizi-risolti\/\"><strong><span style=\"text-decoration: underline;\">formule di prodotto degne di nota<\/span><\/strong><\/a> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-trinomios-al-cuadrado\"><\/span> Esempi di trinomi quadrati<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Una volta che abbiamo visto qual \u00e8 la formula per un trinomio quadrato, vedremo diversi esempi di calcolo del quadrato di un trinomio:<\/p>\n<h3 class=\"wp-block-heading\"> Esempio 1<\/h3>\n<ul>\n<li> Calcola la seguente potenza di un trinomio quadrato:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ee4db6a5192b7efea2342d21275e487_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x^2+x+3\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"101\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> La formula del quadrato di un trinomio \u00e8:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9597e2a9cf6403902d36e5ca6411045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"345\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Pertanto, dobbiamo prima identificare i valori dei parametri<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bfaed44949cf9cfbeb3445de33aabd3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a,b\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> della formula. In questo esercizio<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> Est<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09f6edd3d7af07ab26b4a0a71c20c0b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2,\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"22\" style=\"vertical-align: -4px;\"><\/p>\n<p> il coefficiente<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> corrispondono a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-038741496726a75b03e91a2e030b0287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e8 il termine indipendente 3:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-55e06f44486e75e9153a60d36e83bc37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} (a+b+c)^2\\\\[2ex] \\left(x^2+x+3\\right)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x^2 \\\\[2ex] b=x \\\\[2ex] c=3 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"90\" width=\"343\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> E quando conosciamo gi\u00e0 i valori, sostituiamo semplicemente questi valori nella formula ed eseguiamo i calcoli: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-trinome-au-carre.png\" alt=\"esempio di trinomio quadrato\" class=\"wp-image-2850\" width=\"643\" height=\"224\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> D\u2019altra parte, va notato che un trinomio quadrato non \u00e8 la stessa cosa di <a href=\"https:\/\/mathority.org\/it\/trinomio-quadrato-perfetto\/\"><strong><span style=\"text-decoration: underline;\">un trinomio quadrato perfetto<\/span><\/strong><\/a> . Questo \u00e8 un errore comune, perch\u00e9 molte persone si confondono con questi due concetti. Puoi vedere le differenze tra questi due tipi di trinomi al link in questo paragrafo.<\/p>\n<h3 class=\"wp-block-heading\"> Esempio 2<\/h3>\n<ul>\n<li> Trova il quadrato successivo di un trinomio:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c6ced36e156a021e512b73f322138074_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x^2-2x+4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"110\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Per determinare questa potenza polinomiale dobbiamo applicare la formula del trinomio elevato a due:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9597e2a9cf6403902d36e5ca6411045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"345\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> In questo problema,<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> Ci\u00f2 equivale a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09f6edd3d7af07ab26b4a0a71c20c0b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2,\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"22\" style=\"vertical-align: -4px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> corrisponde al monomio negativo<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae405991eecf234826df9d5bbfb8de4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"36\" style=\"vertical-align: -4px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e8 il numero 4:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e816dc27154d8b4e9748c340da4a04e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} (a+b+c)^2\\\\[2ex] \\left(x^2-2x+4\\right)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x^2 \\\\[2ex] b=-2x \\\\[2ex] c=4 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"90\" width=\"366\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sostituiamo quindi i valori trovati nella formula e risolviamo le operazioni risultanti:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97cdd6092e40172071bcb1e84b4df444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l} \\left(x^2-2x+4\\right)^2 = \\\\[2ex] = \\left(x^2\\right)^2+(-2x)^2+4^2+2\\cdot x^2 \\cdot (-2x) + 2 \\cdot x^2 \\cdot 4 +2 \\cdot (-2x) \\cdot 4 = \\\\[2ex] = x^4+4x^2+16-4x^3 + 8x^2 -16x = \\\\[2ex] = x^4-4x^3+12x^2-16x+16 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"508\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ricorda che la potenza con esponente pari di base negativa d\u00e0 un termine positivo, quindi<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e252311ea5bbe33f6b3f066ed805d4a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-2x)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u00e8 uguale a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dac0d6c1d060e62694d182231bd81d82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ora che hai visto come si calcola il quadrato di un trinomio, probabilmente ti interesser\u00e0 anche sapere come risolvere il <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/formula-del-prodotto-della-somma-per-la-differenza\/\">prodotto della somma per la differenza<\/a><\/span><\/strong> di due termini. In effetti, \u00e8 tra le prime 3 identit\u00e0 degne di nota (pi\u00f9 importanti). Puoi vedere qual \u00e8 la sua formula e come viene applicata nella pagina collegata. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Demostracion-de-la-formula-del-cuadrado-de-un-trinomio\"><\/span> Dimostrazione della formula del quadrato di un trinomio<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Per finire di comprendere la nozione di potenza di un trinomio al quadrato, dedurremo la formula che abbiamo appena studiato.<\/p>\n<p> Da qualsiasi trinomio elevato a 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-379affdd0954c4ca08ed08041e0eb7b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> L&#8217;espressione algebrica sopra equivale a moltiplicare il trinomio tra parentesi per se stesso:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8944601270bfee61c23bb9440e7fd79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2 = (a+b+c)(a+b+c)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"275\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ora moltiplichiamo i due trinomi:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ceaddc98a341af8c426098e15affbe7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)(a+b+c)= a^2+ab+ac+ba+b^2+bc+ca+cb+c^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"505\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Infine, raggruppiamo termini simili:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-79d99fd9567501331249064ee77e6db1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2+ab+ac+ba+b^2+bc+ca+cb+c^2 = a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"576\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> E in questo modo siamo gi\u00e0 arrivati all&#8217;espressione della formula, quindi si dimostra la formula del quadrato di un trinomio:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9597e2a9cf6403902d36e5ca6411045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"345\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sul nostro sito web abbiamo pi\u00f9 dimostrazioni di identit\u00e0 importanti. Ad esempio, puoi vedere la dimostrazione della formula per una <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/quadrato-di-una-somma-o-somma-al-quadrato\/\">somma al quadrato<\/a><\/span><\/strong> e una <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/quadrato-di-una-differenza-o-sottrazione\/\">differenza al quadrato<\/a><\/span><\/strong> . Inoltre, in questi link vedrai non solo le loro dimostrazioni, ma anche l&#8217;interpretazione geometrica delle loro formule, cio\u00e8 cosa significano geometricamente questi tipi di identit\u00e0 notevoli. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-trinomios-al-cuadrado\"><\/span> Risolti problemi sui trinomi quadrati<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Risolvi i seguenti trinomi quadrati: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1e2db1dacfd70bcdf33589968427633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(x^2+x+5\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"132\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6eddfbe2255cd7f5b8d829ff6aef4e38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\left(x^2+3x-4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"141\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-577a572f8974257e1d6d7b8411f75f4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(4x^2-6x+3\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"150\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a26869f17cf7889324d3d5e6755b800_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\left(x^3-3x^2-9x\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"159\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Per risolvere tutti gli esercizi dobbiamo utilizzare la formula del quadrato di un trinomio, che \u00e8: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9597e2a9cf6403902d36e5ca6411045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"345\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-749dc45e7a00d7122d62b774706bdcc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{array}{l} \\left(x^2+x+5\\right)^2 = \\\\[2ex] = \\left(x^2\\right)^2+x^2+5^2+2\\cdot x^2 \\cdot x + 2 \\cdot x^2 \\cdot 5 +2 \\cdot x \\cdot 5 = \\\\[2ex] = x^4+x^2+25+2x^3 + 10x^2 +10x = \\\\[2ex] = \\bm{x^4+2x^3+11x^2+10x+25} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"438\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1f51f18b3c1118b6e8e3acc3441b0ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{array}{l}\\left(x^2+3x-4\\right)^2 = \\\\[2ex] = \\left(x^2\\right)^2+(3x)^2+(-4)^2+2\\cdot x^2 \\cdot 3x + 2 \\cdot x^2 \\cdot (-4) +2 \\cdot 3x \\cdot (-4) = \\\\[2ex] = x^4+9x^2+16+6x^3-8x^2-24x = \\\\[2ex] = \\bm{x^4+6x^3+x^2-24x+16} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"557\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49c6496bf684296d315fc96d9cb5857e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{array}{l}\\left(4x^2-6x+3\\right)^2 = \\\\[2ex] = \\left(4x^2\\right)^2+(-6x)^2+3^2+2\\cdot 4x^2 \\cdot (-6x) + 2 \\cdot 4x^2 \\cdot 3 +2 \\cdot (-6x) \\cdot 3 = \\\\[2ex] = 16x^4+36x^2+9-48x^3+24x^2-36x = \\\\[2ex] = \\bm{16x^4-48x^3+60x^2-36x+9} \\end{array}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"570\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7cd08035d8402c27c411bcf5b30216cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{array}{l}  \\left(x^3-3x^2-9x\\right)^2 = \\\\[2ex] = \\left(x^3\\right)^2+\\left(-3x^2\\right)^2+(-9x)^2+2\\cdot x^3 \\cdot (-3x^2) + 2 \\cdot x^3 \\cdot (-9x) +2 \\cdot (-3x^2) \\cdot (-9x) = \\\\[2ex] = x^6+9x^4+81x^2-6x^5-18x^4+54x^3 = \\\\[2ex] = \\bm{x^6-6x^5-9x^4+54x^3+81x^2} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"682\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In questa pagina spieghiamo come risolvere il quadrato di un trinomio (formula). Inoltre, potrai vedere diversi esempi ed esercitarti con esercizi risolti passo dopo passo di trinomi quadrati. Formula per un trinomio quadrato Logicamente, per comprendere la formula del trinomio al quadrato, devi prima sapere cos&#8217;\u00e8 un trinomio . Ti lascio questo link nel caso &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/trinomio-quadrato\/\"> <span class=\"screen-reader-text\">Trinomio quadrato<\/span> Leggi altro &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[10],"tags":[],"class_list":["post-347","post","type-post","status-publish","format-standard","hentry","category-identita-notevoli"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Trinomio quadrato - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/it\/trinomio-quadrato\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Trinomio quadrato - Mathority\" \/>\n<meta property=\"og:description\" content=\"In questa pagina spieghiamo come risolvere il quadrato di un trinomio (formula). 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