👤

Sagot :

TOMMUS

[tex](a+b+c)^2=((a+b)+c)^2\\(a+b+c)^2=(a+b)^2+2(a+b)c+c^2\\(a+b+c)^2=a^2+2ab+b^2+2ac+2bc+c^2\\(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc[/tex]

PIDIO

Bonjour !

[tex]F= (a+b+c)² \\ = {((a + b) + c)}^{2} [/tex]

On utilise l'identité remarquable (a+b)²=a²+2ab+b² avec a=a+b et b=c

[tex]F = {((a + b) + c)}^{2} \\ = {(a + b)}^{2} + 2(a + b)c + {c}^{2} \\ = {a}^{2} + 2ab + {b}^{2} + 2ac + 2bc + {c}^{2} \\ ={a}^{2} + {b}^{2}+{c}^{2}+2ab + 2ac + 2bc \\= {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + ac + bc)[/tex]

Bonne journée

© 2024 IDNLearn. All rights reserved.