Learn Dutch: Wij hebben de lening bekeken. - We have examined the loan.

Because the infinitive bekijken (to examine/look at) starts with the unstressed prefix be-. Verbs that already start with prefixes like be-, ver-, her-, or ont- are inseparable. This means they do not get the standard ge- added to the beginning of their past participle form.

The infinitive is bekijken. Why does the vowel change to an 'e' in bekeken?

Bekijken is a strong (irregular) verb, following the exact same pattern as its base verb kijken (to look). In Dutch, strong verbs with an -ij- in the infinitive usually change that vowel to a long -e- in the past participle. Therefore, kijken becomes gekeken, and bekijken becomes bekeken.

What is the difference between using kijken and bekijken in a sentence like this?

Kijken simply means "to look", while adding the prefix be- makes it bekijken, meaning "to look at", "to view", or "to examine". Adding be- also makes the verb transitive, meaning it must act directly on an object. You can't just use "look" directly on an object in Dutch (de lening gekeken is incorrect); you have to use bekeken to say you looked at or examined it.