c, Ta có:
\(VP=\left(a+b+c\right)^3=\left[\left(a+b\right)+c\right]^3\)
\(=\left(a+b\right)^3+3\left(a+b\right)^2c+3\left(a+b\right)c^2+c^3\)
\(=\left(a+b\right)^3+c^3+3\left(a+b\right).c.\left(a+b+c\right)\)
\(=a^3+b^3+3a^2b+3ab^2+c^3+3\left(a+b\right).c.\left(a+b+c\right)\)
\(=a^3+b^3+c^3+3ab.\left(a+b\right)+3\left(a+b\right).c\left(a+b+c\right)\)
\(=a^3+b^3+c^3+3\left(a+b\right).\left[ab+c.\left(a+b+c\right)\right]\)
\(=a^3+b^3+c^3+3\left(a+b\right).\left(ab+ac+cb+c^2\right)\)
\(=a^3+b^3+c^3+3\left(a+b\right).\left(ab+ac\right)+\left(cb+c^2\right)\)
\(=a^3+b^3+c^3+3\left(a+b\right).a.\left(b+c\right)+c.\left(b+c\right)\)
\(=a^3+b^3+c^3+3\left(a+b\right)\left(b+c\right)\left(a+c\right)=VT\)
\(\rightarrow\) đpcm
Chúc bạn học tốt!!!
