Question

Chứng minh hằng đẳng thức:

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

Các bn giúp mk vs :))

Ai lm đc mk thì mk cho 3 tick!!!

~~~Kb nx nha~~~

Answer 1

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

==a³+b³+c³+3(a+b)[(ab+ac)+(bc+c2)]

=a³+b³+c³+3(a+b)(a+c)(b+c)

Answer 2

#)Giải :

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

\(=a^3+b^3+c^3+3\left(a+b\right)\left(ab+ac+ca+c^2\right)\)

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

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

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

\(\Rightarrowđpcm\)