How to use Datetime in Dynamic SOQL Query in Salesforce?

This error is because of wrong construction of Dynamic Query with Datetime. following code snippet will give idea on how to construct dynamic query for Datetime ?

//format the datetime to make it Dynamic Soql ready
String formatedDt = cutOffDateTime.format('yyyy-MM-dd'T'HH:mm:ss'Z'');
String sql = 'SELECT  a.Id  FROM  Agents_Answer__c a    WHERE  a.Agents_Test_Result__r.Agent_Name__r.IsActive__c = false AND  LastModifiedDate < '+ formatedDt ;
Where, “cutOffDateTime” is variable of datetime type.