Infix, Postfix and Prefix Algebraic Notations

Infix notation: Operations are written between operands.

A * (B + C)

Usually used by human beings, Infix notation is quite simple to understand, but has one drawback which is you need to use brackets to show the order in which operations should be performed and if you don't do so, you'll get different results and have multiple outcomes for each operation.

Prefix notation: Aka Polish notation, Operations are written before operands.

*A+BC

Can simply be interpreted as start from the first operation and apply it to the next two operands. In order to evaluate the given example and change it to infix notation one would consider:

1. *A+BC: Apply * to A and +BC => A * (+BC)
2. +BC: Apply + to B and C => (B+C)
   

And then follow from 2 to 1 to evaluate the expression.

Postfix notation: AKA Reverse Polish notation, Operations are written after operands.

ABC+*

Can simply be interpreted as "apply the last operation to the first and second operands". In order to evaluate the given example and change it to infix notation one would consider:

1. ABC+*: Apply * to A & BC+ => A * BC+
2. BC+: Apply + to B & C => B + C

And then follow from 2 to 1 to evaluate the expression.