$a^2-b^2$ identity

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.

Proofs

The $a$ squared minus $b$ squared algebraic identity can be derived in two distinct methods.

Algebraic Method

Learn how to prove the $a$ square minus $b$ square rule mathematically in algebraic approach.

Geometric Method

Learn how to derive the $a$ squared minus $b$ squared law mathematically in geometric method.

Verification

Take $a \,=\, 6$ and $b \,=\, 4$. Now, let’s verify the $a$ square minus $b$ square algebraic identity by substituting the values in both side expressions.

$(1).\,\,$ $a^2-b^2$ $\,=\,$ $6^2-4^2$ $\,=\,$ $36-16$ $\,=\,$ $20$

$(2).\,\,$ $(a+b)(a-b)$ $\,=\,$ $(6+4)(6-4)$ $\,=\,$ $10 \times 2$ $\,=\,$ $20$