Question

Tính :

a) \(\left(a+b+c\right)^2\)

b) \(\left(a+b-c\right)^2\)

c) \(\left(a-b-c\right)^2\)

Answer 1

Bài giải:

a) (a + b + c)² = [(a + b) + c]² = (a + b)² + 2(a + b)c + c²

= a²+ 2ab + b² + 2ac + 2bc + c²

= a² + b² + c² + 2ab + 2bc + 2ac.

b) (a + b – c)² = [(a + b) – c]² = (a + b)² - 2(a + b)c + c²

= a² + 2ab + b² - 2ac - 2bc + c²

= a² + b² + c² + 2ab - 2bc - 2ac.

c) (a – b –c)² = [(a – b) – c]² = (a – b)² – 2(a – b)c + c²

= a² – 2ab + b² – 2ac + 2bc + c²

= a² + b² + c² – 2ab + 2bc – 2ac.

Answer 2

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

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

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