1) 
x = Symbol('x')
(x +3) * 2 - 4 - 2 * x + 3

2) 
solve([7*x + 3*(x + 1) - 2*x/4 + 1],x)

3) 
>>> ((x + 1) * ( x + 1)).expand() == x**2 + 2* x + 1
True

>>> ((x - 1) * ( x + 1)).expand() == x**2 - 1
True

4) ((x * (x**2 +5)).subs(x,1)).expand()

((x * (x**2 +5)).subs(x,x+1)).expand()