a² – b² formula

Formula

$a^2-b^2 \,=\, (a+b)(a-b)$

Introduction

$(a+b)(a-b)$ is an algebraic identity and represents the product of two binomials, formed by the summation and subtraction of the literals $a$ and $b$. In mathematics, it is used to write the product of the binomial factors as subtraction of the squares of the literals and vice-versa.

Proof

There are two distinct possible ways to derive the proof of the $(a+b)(a-b)$ algebraic identity in mathematics.

Algebraic Method

Learn how to derive the $(a+b)(a-b)$ formula in algebraic approach on the basis of multiplication of algebraic expressions.

Geometric Method

Learn how to derive the $a^2-b^2$ identity in product form of binomial factors geometrically on the basis of areas of square and rectangle.