Anomalous sound detection systems must detect unknown, atypical sounds using only normal audio data. Conventional methods use the serial method, a combination of outlier exposure (OE), which classifies normal and pseudo-anomalous data and obtains embedding, and inlier modeling (IM), which models the probability distribution of the embedding. Although the serial method shows high performance due to the powerful feature extraction of OE and the robustness of IM, OE still has a problem that doesn't work well when the normal and pseudo-anomalous data are too similar or too different. To explicitly distinguish these data, the proposed method uses multi-task learning of two binary cross-entropies when training OE. The first is a loss that classifies the sound of the target machine to which product it is emitted from, which deals with the case where the normal data and the pseudo-anomalous data are too similar. The second is a loss that identifies whether the sound is emitted from the target machine or not, which deals with the case where the normal data and the pseudo-anomalous data are too different. We perform our experiments with DCASE 2021 Task~2 dataset. Our proposed single-model method outperforms the top-ranked method, which combines multiple models, by 2.1% in AUC.