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{"version":3,"file":"2N41-7b-k2Q3jAMG.js","sources":["../../src/exercices/2e/2N41-7b.js"],"sourcesContent":["import { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { ecritureAlgebrique, reduireAxPlusB } from '../../lib/outils/ecritures'\nimport Exercice from '../deprecatedExercice.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { factorisationCompare } from '../../lib/interactif/comparaisonFonctions'\nimport { handleAnswers } from '../../lib/interactif/gestionInteractif.js'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\n\nexport const titre = 'Factoring with remarkable identities (level II)'\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\n/**\n * Factoriser avec a²-b² avec a ou b expression algébrique 1er degré\n* @author Stéphane Guyon\n* 2N41-7b\n*/\nexport const uuid = '874e8'\nexport const ref = '2N41-7b'\nexport default function FactoriserIdentitesremarquables2 () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.titre = titre\n this.consigne = 'Factor the following expressions.'\n this.nbCols = 1\n this.nbColsCorr = 1\n this.spacing = 1\n this.spacingCorr = 1\n this.nbQuestions = 3\n this.sup = 1\n\n this.nouvelleVersion = function () {\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n let typesDeQuestionsDisponibles = []\n if (this.sup === 1) {\n typesDeQuestionsDisponibles = [1] // (ax+b)²-c²\n }\n if (this.sup === 2) {\n typesDeQuestionsDisponibles = [2] // c²-(ax+b)²\n }\n if (this.sup === 3) {\n typesDeQuestionsDisponibles = [3] // (ax+b)²-(cx+d)²\n }\n if (this.sup === 4) {\n typesDeQuestionsDisponibles = [1, 2, 3] // Mélange des cas précédents\n }\n const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n for (let i = 0, texte, texteCorr, cpt = 0, a, b, c, d, k, typesDeQuestions; i < this.nbQuestions && cpt < 50;) {\n typesDeQuestions = listeTypeDeQuestions[i]\n do {\n a = randint(2, 9) * choice([-1, 1])\n b = randint(1, 9) * choice([-1, 1])\n c = randint(2, 9)\n d = randint(1, 9) * choice([-1, 1])\n } while ((a === c && b === d) || (a === -c && b === -d) || [a, b].filter(el => el < 0).length === 2 || [c, d].filter(el => el < 0).length === 2)\n switch (typesDeQuestions) {\n case 1:\n texte = `$(${a}x${ecritureAlgebrique(b)})^2-${c * c}$` // (ax+b)²-c²\n\n texteCorr = // `$(${a}x${ecritureAlgebrique(b)})^2-${c * c}=(${a}x${ecritureAlgebrique(b)})^2-${c}^2$<br>\n `We recognize the remarkable identity $a^2-b^2=(\\\\color{red}a\\\\color{black}-\\\\color{blue}b)(\\\\color{red}a\\\\color{black}+\\\\color{blue}b)$, with $a=\\\\color{red}${a}x${ecritureAlgebrique(b)}$ and $ b=\\\\color{blue}${c}$.<br><br>$(${a}x${ecritureAlgebrique(b)})^2-${c * c}= (\\\\color{red} ${a}x${ecritureAlgebrique(b)}\\\\color{black})^2-\\\\color{blue} ${c}\\\\color{black}^2 $ <br>$\\\\phantom{(${a}x${ecritureAlgebrique(b)})^2-${c * c}}=\\\\left[\\\\color{red} (${a}x${ecritureAlgebrique(b)})\\\\color{black}-\\\\color {blue} ${c}\\\\right] \\\\left[ \\\\color{red}(${a}x${ecritureAlgebrique(b)})\\\\color{black}+\\\\color{blue}${c}\\\\right] $<br>$\\\\phantom{(${a}x${ecritureAlgebrique(b)} )^2-${c * c}}= (${reduireAxPlusB(a, b - c)}) (${reduireAxPlusB(a, b + c)})$`\n handleAnswers(this, i, { reponse: { value: `(${reduireAxPlusB(a, b - c)}) (${reduireAxPlusB(a, b + c)})`, compare: factorisationCompare } }, { formatInteractif: 'calculation' })\n break\n case 2:\n texte = `$${c * c}-(${a}x${ecritureAlgebrique(b)})^2$` // c²-(ax+b)²\n texteCorr = // `$${c * c}-(${a}x${ecritureAlgebrique(b)})^2=${c}^2-(${a}x${ecritureAlgebrique(b)})^2$<br>\n `We recognize the remarkable identity $a^2-b^2=(\\\\color{red}a\\\\color{black}-\\\\color{blue}b)(\\\\color{red}a\\\\color{black}+\\\\color{blue}b)$, with $a=\\\\color{red}${c}$ and $ b=\\\\color{blue}${a}x${ecritureAlgebrique(b)}$. <br><br>$${c * c}-(${a}x${ecritureAlgebrique(b)})^2= \\\\color{red}${c}\\\\color{black}^2-(\\\\color{blue}${a}x${ecritureAlgebrique(b)}\\\\color{black})^2 $<br>$\\\\phantom{${c * c}-(${a}x${ecritureAlgebrique(b)})^2}=\\\\left[ \\\\color{red}${c}\\\\color{black}-(\\\\color{blue}${a}x${ecritureAlgebrique(b)}\\\\color{black}) \\\\right] \\\\left[ \\\\color{red}${c}\\\\color{black}+(\\\\color{blue}${a}x${ecritureAlgebrique(b)}\\\\color{black}) \\\\right] $<br>$\\\\phantom{${c * c} -(${a}x${ecritureAlgebrique(b)})^2}=(${c}${ecritureAlgebrique(-a)}x${ecritureAlgebrique(-b)}) (${c}${ecritureAlgebrique(a)}x${ecritureAlgebrique(b)})$<br>$\\\\phantom{${c * c}-(${a}x${ecritureAlgebrique(b)})^2}=(${reduireAxPlusB(-a, c - b)}) (${reduireAxPlusB(a, b + c)})$`\n handleAnswers(this, i, { reponse: { value: `(${reduireAxPlusB(-a, c - b)}) (${reduireAxPlusB(a, b + c)})`, compare: factorisationCompare } }, { formatInteractif: 'calculation' })\n break\n case 3: {\n texte = `$(${a}x${ecritureAlgebrique(b)})^2-(${c}x${ecritureAlgebrique(d)})^2$` // (ax+b)²-(cx+d)²\n // $(${a}x${ecritureAlgebrique(b)})^2-(${c}x${ecritureAlgebrique(d)})^2=a^2-b^2$<br>\n texteCorr = `We recognize the remarkable identity $a^2-b^2=(\\\\color{red}a\\\\color{black}-\\\\color{blue}b\\\\color{black})(\\\\color{red }a\\\\color{black}+\\\\color{blue}b\\\\color{black})$, with $a=\\\\color{red}${a}x${ecritureAlgebrique(b)}$ and $b=\\\\color{blue}${c}x${ecritureAlgebrique(d)}$. <br><br>$(${a}x${ecritureAlgebrique(b)})^2-(${c}x${ecritureAlgebrique(d)})^2=\\\\left[ (\\\\color{red}${a}x${ecritureAlgebrique(b)}\\\\color{black})-(\\\\color{blue}${c}x${ecritureAlgebrique(d)}\\\\color {black})\\\\right]\\\\left[ (\\\\color{red}${a}x${ecritureAlgebrique(b)}\\\\color{black})+(\\\\color{blue}${c}x${ecritureAlgebrique(d)}\\\\color{black})\\\\right]$<br>$\\\\phantom{(${a}x${ecritureAlgebrique(b)})^2-(${c}x${ecritureAlgebrique(d)})^2}=(${a}x${ecritureAlgebrique(b)}${ecritureAlgebrique(-c)}x${ecritureAlgebrique(-d)})(${a}x${ecritureAlgebrique(b)}${ecritureAlgebrique(c)}x${ecritureAlgebrique(d)})$<br>`\n\n texteCorr += `$\\\\phantom{(${a}x${ecritureAlgebrique(b)})^2-(${c}x${ecritureAlgebrique(d)})^2}=`\n const facteur1 = reduireAxPlusB(a - c, b - d)\n const facteur2 = reduireAxPlusB(a + c, b + d)\n const facteurConstant = [facteur1, facteur2].filter(el => !el.includes('x'))\n if (facteurConstant.length === 0) {\n texteCorr += `(${facteur1})(${facteur2})$`\n } else {\n if (facteur1.includes('x')) {\n texteCorr += `${facteur2}(${facteur1})$`\n } else {\n texteCorr += `${facteur1}(${facteur2})$`\n }\n }\n handleAnswers(this, i, {\n expr: {\n value: `(${facteur1})(${facteur2})`,\n compare: factorisationCompare\n }\n }, { formatInteractif: 'calculation' })\n } break\n }\n if (this.interactif) {\n texte += ' $=$' + ajouteChampTexteMathLive(this, i, 'inline15 college6e ml-2')\n }\n if (this.questionJamaisPosee(i, a, b, c, d, k, typesDeQuestions)) {\n // If the question has never been asked, we create another one\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n i++\n }\n cpt++\n }\n listeQuestionsToContenu(this)\n }\n this.besoinFormulaireNumerique = ['Difficulty level', 4, '1: form (ax+b)²-c²\\n 2: form c²-(ax+b)²\\n 3: (ax+b)²-(cx+d)²\\n 4: Combination of previous 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