bai toan nay kho

( a + b + c) . ( a + b + c )  - 2 . ( a . b + b.c + c.a )

= a 

Trình bày rõ 

(a+b+c).(a+b+c)-2(a.b+b.c+c.a)=a^2+ab+ca+ab+b^2+bc+ca+bc+c^2-2ab-2bc-2ca=(a^2+b^2+c^2)+(ab+ab-2ab)+(ca+ca-2ca)+(bc+bc-2bc)=a^2+b^2+c^2 .

Mik viết thế này mong bạn thông cảm .

Ta có: \(\left(a+b+c\right).\left(a+b+c\right)-2\left(ab+bc+ca\right)\)

     \(=a^2+b^2+c^2+2\left(ab+bc+ca\right)-2\left(ab+bc+ca\right)\)

     \(=a^2+b^2+c^2\)

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

(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 - 2ab - 2bc - 2ca

= a² + ab + ac + ab + b² + bc + ac + bc + c² - 2ab - 2bc - 2ca

= a² + b² + (ab + ab) + (bc + bc) + (ac + ac) - 2ab - 2bc - 2ca

= a² + b² + 2ab + 2bc + 2ca - 2ab - 2bc - 2ca

= a² + b².