Aplicações dos produtos notáveis na resolução de problemas

Abstract

This paper investigates the applications of remarkable products in solving mathematical problems, highlighting their relevance in the context of teaching and learning. Based on bibliographic research, the study addresses fundamental topics such as exponentiation, root extraction, and algebraic factorization, establishing direct connections with the Brazilian National Common Curricular Base (BNCC), which values the development of logical reasoning, meaningful learning, and contextualized problem-solving. Among the main focuses, the innovative method proposed by student Júlia Pimenta Ferreira for calculating square roots stands out, offering an alternative approach based on the application of the notable product of the square of the sum of two terms. This methodology, besides being accessible and intuitive, demonstrates how creative thinking can significantly contribute to mathematics education and stimulate students’ interest. The study also explores the presence of remarkable products in various fields of knowledge and everyday situations, such as Geometry, Civil Construction, and Agriculture, demonstrating their practical and interdisciplinary nature. In addition, the paper discusses the common challenges in teaching these concepts, such as the excessive emphasis on memorization and the lack of contextualization, which often hinder the development of students’ critical thinking. Based on these challenges, the adoption of active methodologies, the use of educational technologies, and the encouragement of creativity in the classroom are proposed as strategies to make teaching more dynamic, meaningful, and student-centered. Thus, the research highlights the importance of innovative and humanized pedagogical practices that transform mathematics into a tool for students’ intellectual and social empowerment.