How do I simplify polynomial coefficients with symbolic variables to the least possible forms?

I am working on a two-area LFC system. The characteristic polynomials are represented as a function of system parameters (symbolic variables). Here, I want to simplify the polynomial coefficients to their simplest form. I tried using Matlab's "simplify" and "collect" functions, but I was unable to achieve the desired result. I welcome your recommendations.

Answer 1

[John D'Errico]

The simplest form in your eyes is not always what a computer sees as the simplest form. It may require factoring the polynomial to make it looks better. But that need not be easy to find those factors. You can try using the simplify options.

help simplify

 simplify - Algebraic simplification
    This MATLAB function performs algebraic simplification of expr.

    Syntax
      S = simplify(expr)
      S = simplify(expr,Name,Value)

    Input Arguments
      expr - Input expression
        symbolic expression | symbolic function | symbolic vector |
        symbolic matrix

    Name-Value Arguments
      All - Option to return equivalent results
        false (default) | true
      Criterion - Simplification criterion
        'default' (default) | 'preferReal'
      IgnoreAnalyticConstraints - Simplification rules
        false (default) | true
      Seconds - Time limit for the simplification process
        Inf (default) | positive number
      Steps - Number of simplification steps
        1 (default) | positive number

    Examples
      Simplify Expressions
      Simplify Matrix Elements
      Get Simpler Results for Logarithms and Powers
      Get Simpler Results Using More Simplification Steps
      Get Equivalent Results for Symbolic Expression
      Separate Real and Imaginary Parts
      Avoid Imaginary Terms in Exponents
      Simplify Units
      Get Simpler Result by Expanding Expression

    See also collect, combine, expand, factor, horner, numden, rewrite,
      simplifyFraction, Simplify Symbolic Expression

    Introduced in Symbolic Math Toolbox before R2006a
    Documentation for simplify
       doc symbolic/simplify

    Other uses of simplify

       digraph/simplify        InputOutputModel/simplify
       explicitMPC/simplify    polyshape/simplify
       graph/simplify          sym/simplify

For example:

syms x y
P = x^2 + 4*x + 4 + x*y

P = 

But is the expression

(x+2)^2 + x*y

ans = 

a simpler expression? Sometimes simplfy can give you a better result. But here it does not.

simplify(P,'steps',100,'all',true)

ans = 

[Suud Hasen]

I employed the function, but it didn't provide a simplified form. I have manually computed some of the coefficients just for comparison however some of the coefficients are too huge to be manually computed.