Ta có :
\(\left(a+b+c\right)^3-a^3-b^3-c^3\)
\(=\left[\left(a+b\right)+c\right]^3-c^3-\left(a^3+b^3\right)\)
\(=\left(a+b\right)^3+3\left(a+b\right)^2c+3\left(a+b\right)c^2+c^3-c^3-\left(a+b\right)\left(a^2+b^2-ab\right)\)
\(=\left(a+b\right)\left[\left(a+b\right)^2+3\left(a+b\right)c+3c^2-\left(a^2+b^2-ab\right)\right]\)
\(=\left(a+b\right)\left[a^2+b^2+2ab+3ac+3bc+3c^2-a^2-b^2+ab\right]\)
\(=\left(a+b\right)\left[3ab+3ac+3bc+3c^2\right]\)
\(=3\left(a+b\right)\left[a\left(b+c\right)+c\left(b+c\right)\right]\)
\(=3\left(a+b\right)\left(b+c\right)\left(c+a\right)\)
\(\Rightarrow\left(a+b+c\right)^3=a^3+b^3+c^3+3\left(a+b\right)\left(b+c\right)\left(c+a\right)\)
Vậy ...
mình không biết bạn viết kiểu gì luôn.nó cứ ra toàn chữ left roi right thôi bạn ạ
