Difference of Squares of Two Consecutive Even Numbers: A Mathematical Investigation

Ronald S. Decano, Jernel C. Ondong, Liezel P. Vasay and Greatchen L. Medrano
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Ronald S. Decano: Holy Cross of Davao College Center for Research Sta. Ana Ave., Davao City
Jernel C. Ondong: Holy Cross of Davao College Center for Research Sta. Ana Ave., Davao City
Liezel P. Vasay: Holy Cross of Davao College Center for Research Sta. Ana Ave., Davao City
Greatchen L. Medrano: Holy Cross of Davao College Center for Research Sta. Ana Ave., Davao City

International Journal of Research and Innovation in Social Science, 2025, vol. 9, issue 2, 771-780

Abstract: This study investigates the difference of squares between two consecutive even numbers using the formula 4(n+1), derived from the general identity a2−b2 = (a−b) of (a+b). The research aims to uncover more profound insights into this formula’s mathematical properties, sequence behavior, and divisibility characteristics. The study adopts theoretical and computational approaches that validate the formula for fifteen examples of consecutive even numbers. The formula 4(n+1) has been validated for a wide range of even numbers, and its results match the manually computed difference of squares (2n+2)2−(2n)2. For all even 2n, the difference of squares simplifies to 4(n+1), confirming the formula’s accuracy and consistency. The formula 4(n+1) provides valuable insights into number patterns, such as divisibility and arithmetic sequences, highlighting its importance in solving mathematical problems. Its simplicity also makes it a powerful tool for teaching foundational concepts and exploring connections across various areas of mathematics.

Date: 2025
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