(A + B)² − (A − B)² = 4AB Formula – Algebraic Identity Chart

The (A + B)² − (A − B)² = 4AB formula is a fundamental algebraic identity that simplifies the difference between the squares of two binomial expressions. This identity is widely used in algebra, polynomial simplification, equation solving, and competitive mathematics. It enables students to perform calculations quickly and accurately without lengthy expansion.

This formula is an essential part of school mathematics, higher secondary education, engineering, and entrance exam preparation, making it an excellent learning resource for classrooms, coaching centers, and self-study.

Formula

(A + B)² − (A − B)² = 4AB

Derivation

Expanding both expressions:

• (A + B)² = A² + 2AB + B²
• (A − B)² = A² − 2AB + B²

Subtracting the second expression from the first:

(A + B)² − (A − B)² = 4AB