Document expansion (DE) in information retrieval (IR) involves modifying each document in the collection by introducing additional terms into the document. It is particularly useful to improve retrieval of short and noisy documents where the additional terms can improve the description of the document content. Existing approaches to DE assume that documents to be expanded are from a single topic. In the case of multi-topic documents this can lead to a topic bias in terms selected for DE and hence may result in poor retrieval quality due to the lack of coverage of the original document topics in the expanded document. This paper proposes a new DE technique providing a more uniform selection and weighting of DE terms from all constituent topics. We show that our proposed method significantly outperforms the most recently reported relevance model based DE method on a spoken document retrieval task for both manual and automatic speech recognition transcripts.