Question

Chứng minh:

\(\left(a+b+c\right)^3=a^3+b^3+c^3+3\left(a+b\right)\left(b+c\right)\left(a+c\right)\)

Answer 1

(a + b + c)³= ((a + b) + c)³

= (a + b)³ + c³ + 3c(a + b)(a + b + c)

= a³ + b³ + 3ab(a + b) + c³ + 3(a + b)(ac + bc + c²)

= a³ + b³ + c³ + 3(a + b)(ab + ac + bc + c²)

= a³ + b³ + c³ + 3(a + b)(a(b + c) + c(b + c))

= a³ + b³ + c³ + 3(a + b)(b + c)(a + c)