# Very simple algebraic FullSimplify/Simplify problem(s), without even assumptions

I did some digging about FullSimplify but did not find something concrete about my problems and I think they are too elementary to pass.

EXAMPLES START

1)This example is not problematic but I will use it as the prototype.

Input1: -((2 k^2)/3) + 8 k^4 M^2 - 12 k^2 M^2 \[Omega]^2 // FullSimplify.

Output1: 2/3 k^2 (-1 + 6 M^2 (2 k^2 - 3 \[Omega]^2))

which is just fine and what I actually need. Notice that M^2 gets factored.

2)Now a slightly modified version of 1)

Input2: -2 k^2 + 12 k^4 M^2 - 18 k^2 M^2 \[Omega]^2 // FullSimplify

Output2: 2 k^2 (-1 + 6 k^2 M^2 - 9 M^2 \[Omega]^2)

Now this is problematic, notice that M^2 did not get factored in this case as in Output1 and therefore the expression is not fully simplified.

3)A simpler problematic example.

Input3: (2 k^2)/3 - 4 k^4 // FullSimplify

Output3: (2 k^2)/3 - 4 k^4 M^2

In this case no simplification was performed whatsoever, even if you try Simplify Output3 is again the same. For the sake of clarity by simplification I mean that the output should have k^2 factored from both terms.

## EXAMPLES END

Questions:

1)Does anyone have any idea why is this happening in Output2 in contrast to Output1?

2)What about Output3? Isn't it too trivial for FullSimplify to fail?

3)Any possible fixes?

• Output 3 has the same leaf count as the result you were expecting.Output 2 has either the same, or one less, depending on exactly where minus signs get placed. These details will affect the eventual result. – Daniel Lichtblau Apr 20 at 14:36