import sympy
sympy.init_session()

x11, x12, x13, x21, x22, x23, x31, x32, x33 = symbols('x_1:4(1:4)')

A = Matrix(3,3,symbols('x_1:4(1:4)'))
expr1 = A.det()

expr2 = x11*(x22*x33 - x23*x32) - x12*(x21*x33 -x23*x31) + x13*(x21*x32 - 
x22*x31)

# How to get expr2 from expr1?

I would like to use sympy to rewrite expressions just like how people would 
commonly do when writing proofs or doing homework. What are the 
documentation that I must read so that I can be proficient at this?

I've read the tutorial and some of the modules in the module reference 
<http://docs.sympy.org/dev/modules/index.html> but feel that I have just 
barely touched the surface of sympy's capabilities. For example, in the 
above code snippet, I don't know how to manipulate expr1 to get expr2. I 
thought expr1.factor() would work but it didn't.

Please advise.

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