python - expand strings as algebraic expressions -

i have set of simple strings, represents dsl:

my_str = ['("word 1" + "word 2") * "word 3"',           '("word 1" + "word 2") * ("word 3" + "word 4")',           '(("word 1" + "word 2") * ("word 3" + "word 4")) * "word 5"',          ] 

i trying (and failing badly) change these more straight forward form such

a = foo(my_str) a= [  '("word 1" * "word 3") + ("word 2" * "word 3")',  '("word 1" * "word 3") + ("word 1" * "word 4") + ("word 2" * "word 3") + ("word 2" * "word 4")',  '("word 1" * "word 3" * "word 5") + ("word 1" * "word 4" * "word 5") + ("word 2" * "word 3" * "word 5") + ("word 2" * "word 4" * "word 5")', ] 

may simple can't seem head around logic.

ok in end used combination of sympy , pyparsing. used pyparsing understand relationships , hierarchies between variables, , sympy create , expand expression.

some 1 interested in bit over-done code can have @ gist here.