import{E as k,c as f,aj as m,r as d,h as v,a0 as b,a as C,s as D,l as Q}from"./index-hc8lvKav.js";import{d as i,t as a}from"./deprecatedFractions-crf_vsDW.js";const q=!0,y="mathLive",T="Développer (a+b)²",O="877a9",L="2N41-4";function N(){k.call(this),this.titre=T,this.consigne="Développer puis réduire les expressions suivantes.",this.nbCols=1,this.nbColsCorr=1,this.spacing=1,this.spacingCorr=1,this.nbQuestions=3,this.sup=5,this.interactifReady=q,this.interactifType=y,this.correctionDetailleeDisponible=!0,f.isHtml?this.spacingCorr=3:this.spacingCorr=2,f.isHtml||(this.correctionDetaillee=!1),this.nouvelleVersion=function(){this.sup=parseInt(this.sup),this.listeQuestions=[],this.listeCorrections=[];const u=[[1,2],[1,3],[2,3],[1,4],[3,4],[1,5],[2,5],[3,5],[4,5],[1,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[3,8],[5,8],[7,8],[1,9],[2,9],[4,9],[5,9],[7,9],[8,9],[1,10],[3,10],[7,10],[9,10]];let s=[];this.sup===1?s=[1]:this.sup===2?s=[2]:this.sup===3?s=[3]:this.sup===4?s=[4]:s=[1,2,3,4];const g=m(s,this.nbQuestions);for(let $=0,c,t,n,p=0,e,o,x=[],r,l,h;$<this.nbQuestions&&p<50;){switch(h=g[$],e=d(1,12),o=d(2,12),x=v(u),r=x[0],l=x[1],t="",h){case 1:c=`$\\left(x+${e}\\right)^2$`,this.correctionDetaillee?(t+=`On développe l'expression en utilisant l'identité remarquable $(a+b)^2=a^2+2ab+b^2$, <br> avec $\\color{red} a = x\\color{black}$ et $\\color{green} b = ${e} \\color{black} $ : <br> <br>`,t+=`$\\left(\\color{red}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2=\\color{red}x\\color{black}^2+2 \\times \\color{red}x \\color{black}\\times \\color{green}${e} \\color{black}+ \\color{green}${e}\\color{black}^2$ <br>`,t+=`$\\phantom{\\left(\\color{red}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2} = x^2+${2*e}x+${e*e}$`):t+=`$\\left(x+${e} \\right)^2=x^2+${2*e}x+${e*e}$`,n=`x^2+${2*e}x+${e*e}`;break;case 2:c=`$\\left(${o}x+${e}\\right)^2$`,this.correctionDetaillee?(t+=`On développe l'expression en utilisant l'identité remarquable $(a+b)^2=a^2+2ab+b^2$, <br> avec $\\color{red} a = ${o}x\\color{black}$ et $\\color{green} b = ${e} \\color{black} $ : <br> <br>`,t+=`$\\left(\\color{red}${o}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2 = \\left(\\color{red}${o}x\\color{black}\\right)^2 + 2 \\times \\color{red}${o}x\\color{black} \\times \\color{green}${e} + ${e}\\color{black}^2$ <br>`,t+=`$\\phantom{\\left(\\color{red}${o}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2} = ${o*o}x^2+${2*o*e}x+${e*e}$`):t+=`$\\left(${o}x+${e}\\right)^2 = ${o*o}x^2+${2*o*e}x+${e*e}$`,n=`${o*o}x^2+${2*o*e}x+${e*e}`;break;case 3:o=-o,c=`$\\left(${o}x+${e}\\right)^2$`,this.correctionDetaillee?(t+=`On développe l'expression en utilisant l'identité remarquable $(a+b)^2=a^2+2ab+b^2$, <br> avec $\\color{red} a = ${o}x\\color{black}$ et $\\color{green} b = ${e} \\color{black} $ : <br> <br>`,t+=`$\\left(\\color{red}${o}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2 = \\left(\\color{red}${o}x\\color{black}\\right)^2 + 2 \\times \\color{red}(${o}x)\\color{black} \\times \\color{green}${e} + ${e}\\color{black}^2$ <br>`,t+=`$\\phantom{\\left(\\color{red}${o}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2} = ${o*o}x^2 -${2*-o*e}x+${e*e}$`):t=c+`$= ${o*o}x^2 -${2*-o*e}x+${e*e}$`,n=`${o*o}x^2-${2*-o*e}x+${e*e}`;break;case 4:c=`$\\left(${i(r,l)}x+${e}\\right)^2$`,this.correctionDetaillee?(t+=`On développe l'expression en utilisant l'identité remarquable $(a+b)^2=a^2+2ab+b^2$, <br> avec $\\color{red} a = ${i(r,l)}x\\color{black}$ et $\\color{green} b = ${e} \\color{black} $ : <br> <br>`,t+=`$\\left(\\color{red}${i(r,l)}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2 = \\left(\\color{red}${i(r,l)}x\\color{black}\\right)^2 + 2 \\times \\color{red}${i(r,l)}x\\color{black} \\times \\color{green}${e} + ${e}\\color{black}^2 $ <br><br>`,t+=`$\\phantom{\\left(\\color{red}${i(r,l)}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2} = ${i(r*r,l*l)}x^2+${i(2*r*e,l)}x+${e*e}$`,(b(r,l)!==1||b(2*r*e,l)!==1)&&(t+=`<br> <br> $\\phantom{\\left(\\color{red}${i(r,l)}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2} = ${a(r*r,l*l)}x^2+${a(2*r*e,l)}x+${e*e}$`)):(t=c+`$= ${i(r*r,l*l)}x^2+${i(2*r*e,l)}x+${e*e}$`,(b(r,l)!==1||b(2*r*e,l)!==1)&&(t+=`<br> <br> $\\phantom{\\left(\\color{red}${i(r,l)}x\\color{black}+\\color{green}${e}\\color{black}\\right)^2} = ${a(r*r,l*l)}x^2+${a(2*r*e,l)}x+${e*e}$`)),n=[`${i(r*r,l*l)}x^2+${i(2*r*e,l)}x+${e*e}`,`${a(r*r,l*l)}x^2+${a(2*r*e,l)}x+${e*e}`];break}c+=C(this,$),D(this,$,n),this.questionJamaisPosee($,h,e)&&(this.listeQuestions.push(c),this.listeCorrections.push(t),$++),p++}Q(this)},this.besoinFormulaireNumerique=["Niveau de difficulté",5,`1 : Coefficient de x égal à 1
 2 : Coefficient de x supérieur à 1
 3 : Coefficient de x négatif
 4 : Coefficient de x rationnel
 5 : Mélange des cas précédents`]}export{N as default,q as interactifReady,y as interactifType,L as ref,T as titre,O as uuid};
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