When to use split and split up

Solution 1:

Generally speaking, "split up" involves moving two or more things away from each other, where "split" involves a simple division that may or may not mean the parts are detached.

For example:

1. Let's split up to find the pirate booty.
2. Let's split the pirate booty into four equal shares of dubloons.
3. Let's split up the pirate booty.

In the first sentence, the group will separate and each person will search their own area. This kind of division means that the pieces will detach or come away from the whole.

In the second sentence, the booty will be divided into portions, but the dubloons are piled up on a table for instance. No one has taken their share yet.

In the third sentence, the booty is divided in order to be taken away by members of the group.

In your example, you would want to use

We need to split the background image of the website into two parts.

because the two parts will be divided, but remain together.

Solution 2:

Excellent question, I remember wondering about that some time ago.

According to the New Oxford American Dictionary, split up refers to the division of a group of people (the family was split up), or to a couple breaking up (I split up with my boyfriend a year ago). Other than that, it is just split.

Other dictionaries are more liberal with the use of up, including Dictionary.com and thefreedictionary.com. The former says:

4. to divide into distinct parts or portions (often followed by “up”): We split up our rations.

The later gives as example: “This poem doesn't split up into stanzas very well”.