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

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.

$7$ 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.

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.

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

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

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved