Agile methods and software product line engineering (SPLE) are widely recognized as practical approaches for delivering high-quality software, adapting to evolving stakeholder needs, and tackling complex problems. This study proposes a hybrid agile software development and reuse approach called SPLE-Scrum based on the activities of software product line engineering and Scrum. Within the SPLE process, we incorporate requirement engineering and design practices to create a reference architecture with reusable components called core assets by introducing a product management meeting. The core assets are reused to build a series of applications with various product lines. The product increments are delivered in each Sprint with the review and retrospective meetings based on Scrum lifecycle and practices. We present a case study involving a blockchain online store to demonstrate the practical application of SPLE-Scrum, highlighting the benefits of integrating Scrum and software product line engineering. The research hypotheses of the proposed approach were validated through a study of structured interviews with 5 experts and 44 software practitioners, showing that the key factors of product management, project requirements, and product architecture in the SPLE-Scrum approach have a beneficial impact on project success. The SPLE-Scrum approach provides valuable insights and practical guidance for organizations seeking to optimize their software engineering practices while incorporating agile development and software reuse capabilities.