Ta có :
\(\left(a+b+c\right)\left(a+b+c\right)-2\left(ab+bc+ca\right)\)
\(=a^2+ab+ac+ba+b^2+bc+ca+cb+c^2-2ab-2bc-2ca\)
\(=\left(a^2+b^2+c^2\right)+\left(ab+ac+ba+bc+ca+cb-2ab-2bc-2ca\right)\)
\(=a^2+b^2+c^2\)
\(\left(a+b+c\right).\left(a+b+c\right)-2.\left(a.b+b.c+c.a\right)\)
\(=a^2+b^2+c^2-\left(2ab+2bc+2ca\right)\)
\(=a^2+b^2+c^2-2ab-2bc-2ca\)
\(=a^2-2ab+b^2-2bc+c^2-2ca\)
\(=\left(a-2b\right)a+\left(b-2c\right)b+\left(c-2a\right)c\)
Chúc bn học tốt
\(\text{(a+b+c).(a+b+c)-2(a.b+b.c+c.a}\)
\(=a.a+a.b+a.c+b.a+b.b+b.c+c.a+c.b+c.c-2.\left(a.b+b.c+c.a\right)\)
\(=\left(a^2+b^2+c^2\right)+a.b+a.c+b.a++b.c+c.a+c.b-2.a.b-2.b.c-c.a.2\)
\(=a^2+b^2+c^2\)
Vậy.......
Học tốt!
Mk xin lỗi mk sai rồi
\(\left(a+b+c\right).\left(a+b+c\right)-2.\left(ab+bc+ca\right)\)
\(=a^2+ab+ac+ba+b^2+bc+ca+cb+c^2-\left(2ab+2bc+2ca\right)\)
\(=a^2+b^2+c^2+2ab+2bc+2ca-2ab-2bc-2ca\)
\(=a^2+b^2+c^2\)
Chúc bn học tốt
