As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a + b)[superscript 3] = a[superscript 3] + 3a[superscript 2]b + 3ab[superscript 2] + b[superscript 3]" can be generalized from quantitative reasoning in the context of combinatorics problems like the Card Problem (Tillema and Burch 2020). The article then illustrates how the combinatorial reasoning students develop in the Card Problem can support them to see combinatorial structure across algebraic computations. Throughout the article, the authors share work from students and teachers with whom the approach was developed.