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If I start with the following symbolic expression:
a^2 + 2*a*b + b^2
Then run simplify (or factor), I get the expected result:
>> simplify(a^2 + 2*a*b + b^2)
(a + b)^2
Now when I run the same example, but adding another term, no factorisation occurs:
>> simplify(a^2 + 2*a*b + b^2 + 1)
a^2 + 2*a*b + b^2 + 1
How can I get these functions to return the more practical version of this expression ((a + b)^2 + 1)? I have tried all of the obvious options with these functions (like 'Steps', 'IgnoreAnalyticConstraints', etc.) but to no avail.
Context: I have the expression ax^2 - 2*ax*bx + bx^2 + ay^2 - 2*ay*by + by^2 which I need to convert back into (ax - bx)^2 + (ay - by)^2 so it can then be treated correctly as r^2. I know I could use some blunt substitution rules, but for something so simple I feel like I'm missing an obvious 'non-hack' solution.
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If x is an integer, factor returns the prime factorization of x . If x is a symbolic expression, factor returns the subexpressions that are factors of x . F = factor( x , vars ) returns an array of factors F , where vars specifies the variables of interest.
F = symsum( f , k , a , b ) returns the sum of the series f with respect to the summation index k from the lower bound a to the upper bound b . If you do not specify k , symsum uses the variable determined by symvar as the summation index. If f is a constant, then the default variable is x .
S = simplify( expr ) performs algebraic simplification of expr . If expr is a symbolic vector or matrix, this function simplifies each element of expr . S = simplify( expr , Name,Value ) performs algebraic simplification of expr using additional options specified by one or more Name,Value pair arguments.
Symbolic Math Toolbox™ enables you to perform symbolic computations from the MATLAB® command line by defining a special data type — symbolic objects. Functions are called using the familiar MATLAB syntax and are available for integration, differentiation, simplification, equation solving, and other mathematical tasks.
you can run simplify on the two terms separately.
simplify(ax^2 - 2*ax*bx + bx^2) + simplify(ay^2 - 2*ay*by + by^2)
It seems like you already know how it should be simplified anyway.
Also, you eventually want to write it as r^2. This is not generally possible for all second-order expressions, so don't bother trying to find a general solution.
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