Khai triển vế phải ta có :
\(VP=\left(a+b\right)^3-3ab\left(a+b\right)=a^3+3a^2b+3ab^2+b^3-3a^2b-3b^2=a^3+b^3=VT\)
Ta có:
A3 + B3
= A3 + 3A2B + 3AB2 + B3 - 3A2B - 3AB2
= (A + B)3 - (3A2B + 3AB2)
= (A + B)3 - 3AB(A + B)
Vậy...
\(A^3+B^3=\left(A+B\right)^3-3AB\left(A+B\right)\)
\(\Leftrightarrow A^3+B^3=\left(A^3+3A^2B+3AB^2+B^2\right)-\left(3A^2B+3AB^2\right)\)
\(\Leftrightarrow A^3+B^3=A^3+3A^2B+3AB^2+B^2-3A^2B-3AB^2\)
\(\Leftrightarrow A^3+B^3=A^3+B^3\)
\(\Rightarrow........................\left(đcpcm\right)\)
\(\left(a+b\right)^3-3ab\left(a+b\right)\)
\(=a^3+3a^2b+3b^2a+b^3-3a^2b-3b^2a\)
\(=a^3+b^3\left(đpcm\right)\)