Removing Brackets Maths Help

What algorithm I can use to remove all brackets from math expression and still have valid math expression?

Reverse Polish Notation.  RPN.  ...named for Jan Łukasiewicz.Accumulate values in one direction (push each onto a stack) while applying operations in the other. (discarding the values and replacing them with the result)  For example:Algebra: (24 + 6) / (3 * sqrt(25))
          ...becomes the sequence...RPN: 24 6 + 3 25 sqrt * /
Where each value gets pushed onto the stack and each operator processes and discards its arguments and replaces them with the result of the operation.So the above RPN is evaluated as...push the value 24 onto a stack
push the value 6 onto that stack
add the top two values (24 and 6) and replace them on the stack with the result (30)
push the value 3 onto the stack
push the value 25 onto the stack
take the sqrt of the top value (25) and replace it on the stack with that on the stack (5)
multiply the top two values (3 and 5) and replace them on the stack with the result (15)
divide the top value on the stack (15) into the value beneath it (30), replacing them on the stack with the result (2)
Now, all that's left on the stack is the answer. (2)You can use RPN to eliminate all grouping operators. In fact that is how a compiler deals with the evaluation of math expressions. If you want to code this up, search for Recursive Descent Parser - a very simple algorithm that makes this easy.  Okay, the OP has now updated his question with an example that appears to show that he/she is not looking just for a solution that eliminates the brackets/parenthesis but, instead, is looking for an expansion of terms.  If that is indeed the question, it looks like Richard Morris has provided a good solution.

How can you use parentheses and brackets in [math]\LaTeX[/math]?

For parentheses and brackets, you can write[math]1^\text{st}[/math] Bracket:[math]\LaTeX[/math] code: \left( \frac{x}{y} \right) Output: [math]\left( \frac{x}{y} \right)[/math][math]2^\text{nd}[/math] Bracket:[math]\LaTeX[/math] code: \left\{ \frac{x}{y} \right\} Output:[math]\left\{ \frac{x}{y} \right\}[/math][math]3^\text{rd}[/math] Bracket:[math]\LaTeX[/math] code: \left[ \frac{x}{y} \right] Output: [math]\left[ \frac{x}{y} \right][/math]Besides,[math]\LaTeX[/math] code: \left< \frac{x}{y} \right> Output: [math]\left< \frac{x}{y} \right>[/math]** this < and > can be replaced by \langle and \rangle respectively.Those \left and \right commands are used to adjust the sizes automatically. But if you want to adjust their size explicitly, you follow this codes in this table below:[math]\begin{array}{|c|c} \LaTeX \,\text{Code} & \text{Output} \\ \hline \text{\big( \Big( \bigg( \Bigg(}\, - \text{\Bigg) \bigg) \Big) \big)} & \big( \Big( \bigg( \Bigg( - \Bigg) \bigg) \Big) \big) & \\ \text{\big\{ \Big\{ \bigg\{ \Bigg\{}\, - \text{\Bigg\} \bigg\} \Big\} \big\}} & \big\{ \Big\{ \bigg\{ \Bigg\{ - \Bigg\} \bigg\} \Big\} \big\} & \\ \text{\big[ \Big[ \bigg[ \Bigg[}\, - \text{\Bigg] \bigg] \Big] \big]} & \big[ \Big[ \bigg[ \Bigg[ - \Bigg] \bigg] \Big] \big] & \\ \text{\big< \Big< \bigg< \Bigg<}\, - \text{\Bigg> \bigg> \Big> \big>} & \big< \Big< \bigg< \Bigg< - \Bigg> \bigg> \Big> \big> & \\ \end{array}[/math]Moreover,\tiny )
\Tiny \}
\scriptsize ]
\small )
\normalsize \}
\large ]
\Large )
\LARGE \}
\huge ]
\Huge )
For more [math]\LaTeX[/math] you can visit this links:An introduction to beautiful math on QuoraShareLaTeX, Online LaTeX EditorGood luck.