How do i do the reverse from expand function ?

I have an expression lets say

a^2_2*a*b+b^2+b

and i want to simplify the expression to get

(a+b)^2+b

what is the proper way of doing this ?

Answer 1

[Chidvi Modala]

Hi Tomer,

In general, you may use simplify(expr) function to perform algebraic simplification of expr. But simplify currently has some known issue with the simplification of sums. It cannot simplify your entire expression "a^2+2*a*b+b^2+b", but it can simplify "a^2+2*a*b+b^2" to "(a+b)^2". You may use the following example as a workaround.

syms a b;
simplify(expand(a^2+2*a*b+b^2)) + b

[Elif Cansu]

Hi Chidvi,

I was wondering if there has been any improvement with the aforementioned issue. Is there anyway to work around this if we don't know in advance which subcomponent of the expression can be simplified (unlike the case in the answer above)?

[John D'Errico]

@Elif Cansu

No. Simplify still does not see how to return a partially factored result. I would have tried this:

syms a b
expr = a^2+2*a*b+b^2+b;
simplify(expr,steps = 1000,All = true)

ans = 

as the standard way to solve it using simplfy, to see if it would find an alternate form.

But as you can see, it finds no "simpler" way to write that expression. The above was done using the Matlab version in Answers of R2023b.

[Stephen23]

It all depends on what metric you are using to define the term "simpler". According to some metrics you might come up with, using the parentheses could be considered more complex:

https://en.wikipedia.org/wiki/Shunting_yard_algorithm

Expecting a computer to read minds and replicate nebulous human concepts... perhaps we need to involve some AI engine here: proposed new AI-based command SHOWMETHISLIKEIWOULDSEEITINATEXTBOOK().