There are 5 STEPS of turning the Active into the Passive.
The Active: They opened this shop in 2010. 
Step 1. Let's divide the sentence into parts.
they openedthis shopin 2010
Step 2. Object becomes Subject. -
this shop
Step 3. We change the Active form of the Verb into the Passive form of the Verb: 
  • Formula of any Passive - be + V3
the verb opened is in Past Simple. Formula of Past Simple Passive was/were + V3
  • Let's choose the correct "be": "this shop" - "it", so we choose - was
(was: I, he, she, it / were: we, you, they)
  • Let's choose V3:
our verb is opened, so
the 3rd form of the verb "open" is "opened".
Step 4. Do we need to write "by them" here?
No. Because this information is not here.
We do not usually use "by them/by people/by somebody/by someone...".
Step 5. Let's connect all the parts.
SubjectVerbby ...Where/When
this shopwas opened   -in 2010
So the Passive - This shop was opened in 2010.