Math Doubts

Difference of squares formula

Formula

$(1) \,\,\,$ $a^2-b^2$ $\,=\,$ ${(a+b)}{(a-b)}$

$(2) \,\,\,$ $x^2-y^2$ $\,=\,$ ${(x+y)}{(x-y)}$

The formula for the difference of squares is usually represented by $a^2-b^2$ or $x^2-y^2$ algebraically in mathematics. It can be factored as the product of two binomials whose terms are connected by opposite signs.

Introduction

$a$ and $b$ are two terms, and they form two binomials $a+b$ and $a-b$ by connecting both terms with opposite signs. The difference of two terms is $a^2-b^2$ and it can be factored as the product of both binomials by the factorization.

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

The difference of two terms formula is also written in terms of $x$ and $y$ alternatively.

$x^2-y^2$ $\,=\,$ ${(x+y)}{(x-y)}$

So, you can use any one of them to express a formula for the difference of two square terms in mathematics. This identity in algebraic form is most important for factoring difference of any two terms.

Proof



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