Square of the Difference

The difference of any two quantities raised to the power of $2$ is called square of the difference.

Introduction

In Arithmetic, calculating difference of two numbers and squaring a number are two basic mathematical operations. The combination of both mathematical operations are used in some cases to find the square of difference of them.

Example

$7$ and $4$ are two numbers and let’s calculate the square of the difference of them.

${(7-4)}^2 \,=\, 3^2$
$\implies$ ${(7-4)}^2 \,=\, 3 \times 3$
$\,\,\, \therefore \,\,\,\,\,\,$ ${(7-4)}^2 \,=\, 9$

In this way, we calculate square of the difference of any two numbers in the basic mathematics.

Formula

We use terms instead of numbers in advanced mathematics and it is not possible to find the square of the difference of any two terms same as finding the square of difference of two numbers. Therefore, an identity is required in mathematical form for using it as a formula in finding the square of difference of any two terms. The formula for square of difference of terms is written in the following two forms.

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

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