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Which characters belong together here?
我们一定要把写字和书法区分开来。
We must differentiate between writing and calligraphy.
We must draw a distinction between writing and calligraphy.
We must separate (区分开来） writing from calligraphy.
区分：differentiate, distinguish between, draw a distinction
分开：separate
区分开来：separate from??
In () may belong together. I think 3. is maybe the correct analysis.
1a. 我们一定要把（写字区）和（书法区）分开来。
1b. 我们一定要把写字和书法区（分开来）。
我们一定要把写字和书法（区分）开来。
我们一定要把写字和书法（区分开来）。
区分 is the verb, to differentiate.
开 is a resultant complementary, apart.
来 is another resultant complementary, henceforth.
开来 commonly appear together in phrases similar to this one, but they do not form a word. (There is a word 开来 as in 继往开来 which is different).
The affinity of characters is (((区分)开)来) where only 区分 is a word.
The structure is:
区分 main verb (= differentiate)
开来 composite directional complement
Directional complements are movement verbs as:
They work pretty much as result complements, i.e. placed after the main verb, except that they express the direction in which the verb proceeds. Sometimes the meaning is figurative, as in 下去 (= continue).
Furthermore, directional complements can be simple or composite.
In the latter case they are followed by either 去 (go) or 来 (come) to specify the direction of the movement.
A few directional verbs may take only one direction to make the composite form, e.g. 起来 and 开来。
The usage of the composite form is often required with two-character main verbs, therefore here you have 区分开来 (literally, differentiate apart).
“区分开来”经常简写成“区分”或“区分开”。
它和“分开”有些区别，可以这样理解：“区分=区别+分开”，同义词是“辨别”；“分开”，即你所说的“separate”，重点是“分离”，缺少了“辨别”的意味。
As a Chinese, I find it very happy to see this question, let me answer this XD Sentence is '我们一定要把写字和书法区分开来。' In Chinese semantics, It equals '我们一定要把写字和书法区分开。' so the right result is '我们一定要把写字和书法（区分开来）。'
Hi I'm not 100% sure this is what you are asking, but I'll try to explain.
The sentence:
We must differentiate between writing and calligraphy. 我们一定要把写字和书法区分开来.
Breakdown to the phrases
我们(we)一定(must) 要把 写字(writing)和(and)书法(calligraphy)区分(differentiate) 开来.
These are the core phrases of the sentence
In "区分开来", "开来" carried meaning "split"(in context, means seeing writing and calligraphy separately). However if you say that sentence in Chinese without "开来", the sentence still means the same thing.
I hope this helps.
