Difference of squares

A squared quantity subtracted from another squared quantity is called the difference of squares.

Introduction

In mathematics, the squares of two numbers are often involved in subtraction. The difference between squares of both numbers is called as the difference of two squares or simply difference of squares.

Example

$5$ and $3$ are two numbers and the difference of squares of them is written in mathematics as follows.

$5^2-3^2$

$\implies$ $5^2-3^2$ $\,=\,$ $25-9$

$\implies$ $5^2-3^2$ $\,=\,$ $16$

In this way, the difference of squares of any two quantities is calculated mathematically in the basic mathematics.

In advanced mathematics, the difference of two squares is expressed in general form by writing it in the form of two terms but it is not possible to find the difference of squares of them, same as the above due to the unknown quantities of the terms. However, it is most useful in simplifying the complex functions in some cases by writing it into its equivalent form.

At this time, don’t think about it much more but soon you will understand how important it is in mathematics.

Formula

In algebra, the difference of squares is written in two forms and they are $a^2-b^2$ and $x^2-y^2$. You can use any one of them to represent the difference of two squares in general form. Now, learn how to express it into its equivalent form with proof.