1. \(\left(A+B\right)^2=A^2+2AB+B^2\)
2. \(\left(A-B\right)^2=A^2-2AB+B^2\)
3. \(A^2-B^2=\left(A-B\right)\left(A+B\right)\)
4. \(A^3-B^3=\left(A-B\right)\left(A^2+AB+B^2\right)\)
5. \(A^2+B^2=\left(A+B\right)\left(A^2-AB+B^2\right)\)
6. \(\left(A+B\right)^3=A^3+3A^2B+3AB^2+B^3\)
7. \(\left(A-B\right)^2=A^3-3A^2B+3AB^2-B^3\)