Question

x3-y3 .What is the algebraic identity for this equation??

Answer 1

Step-by-step explanation:

If it helps you follow me and mark my answer as brainliest

Answer 2

Concept:

We need to recall the concept of identity to answer this question.

An identity is an equality which is true for all values of the variables.

Given:

The given expression is :   $x^{3} -y^{3}$ .

To find:

The algebraic identity for the given expression.

Solution:

We will use the identity $(x-y)^{3} = x^3-y^3-3xy(x-y)$

On rearranging the terms we have,

                                         $x^{3} -y^{3}$ = $(x-y)^{3}+3xy(x-y)$

                                                     = $(x-y)$ $((x-y)^2+3xy)$

                                                     = $(x-y)$ $(x^2+y^2-2xy +3xy)$    

                                                        (using identity $(x-y)^{2}=x^{2}+y^{2}-2xy$ )

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

Hence, the algebraic identity for $x^{3} -y^{3}$ is $(x-y)$ $(x^{2}+y^{2}+xy)$.