Could Mathematica analytically work with operators (such as $\nabla$) and vectors?

Question

I have the following expression: $$(\nabla+\vec{P})^2$$ where $P=(r\cos\theta sin\phi,r^4\sin\theta,r\cos^3\phi)$

I would like to open the brackets and simplify the expression.

Are there in Mathematica ways analytically do it?

Answer 1

I think the expression should correctly be $(\nabla +P)\cdot( \nabla +P)$

Expression without brackets follows to $ \nabla \cdot \nabla +\nabla \cdot P+P \cdot \nabla + P \cdot P $