Question

Chứng ming hằng đẳng thức 

(a+b+c)³=a³+b³+c³+3(a+b)*(b+c)*(c+a)

Giúp mk nhé

Answer 1

Biến đổi vế trái ta có: 

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

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

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

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

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

=>đpcm