Given $x y + x z + * y z * +$ recover the tree, write it in usual notation and simplify
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Given the boolean expression given in reverse Polish notation $$x y + x z + * y z * +$$ recover the tree, write it in usual notation and simplify. The usual notation is $$begin{array}{ll} &x y + x z + * y z * +\ iff&(x+y) x z + * y z * +\ iff&((x+y)+x) z * y z * +\ iff&(((x+y)+x)*z) y z * +\ iff&(((x+y)+x)*z) (y*z) +\ iff&(((x+y)+x)*z)+(y*z)\ end{array}$$ The recovery tree is Finally, the simplification is $$begin{array}{ll} &(((x+y)+x)*z)+(y*z)\ iff&(2*x+y)*z+y*z\ iff&2*x*z+y*z+y*z\ iff&2*z*(x+y) end{array}$$ Is that correct? Is it possible to write $2*xequiv2x$ and so on? Thanks!
discrete-mathematics trees polish-notation