What is the missing auxiliary verb in this sentence: "The cake ___ been eaten by the children"?

In the sentence "The cake ___ been eaten by the children," the correct auxiliary verb to fill in the blank is "has." This is because the sentence is using the present perfect tense, which describes actions that have occurred at some indefinite point in the past and are relevant to the present. The structure of the present perfect in passive voice requires the use of "has" or "have," followed by the past participle of the main verb.

In this context, "has been eaten" indicates that the action of eating has relevance or consequence at the present moment—most likely that the cake is no longer available. The form "has been" is used because the subject "the cake" is singular, requiring the singular form of the auxiliary verb.

The other options would not create the intended meaning. "Is been eaten" is ungrammatical, as "is" does not serve to form the perfect aspect. "Was been eaten" is also incorrect, as both "was" and "been" cannot be used together in this manner; "was" would indicate past tense, while "been" is the perfect participle and cannot follow "was" without changing the structure. Lastly, "will been eaten" does not fit the grammatical