Question

Verify x cube minus y cube equal to x minus y Into X square + xy + Y square.
(x^3-y^3)= (x-y) (x^2+xy+y^2)
A little quick please!

Answer 1

Solving L.H.S
x(x^2+xy+y^2)-y(x^2+xy+y^2)
=x^3+x^2y+xy^2-yx^2-xy^2-y^3
=x^3+x^2y-yx^2+xy^2-xy^2-y^3
=x^3-y^3

L.H.S=R.H.S

Mark me as brainliest and comment for help

Answer 2

Given:

An equation is given to us which is   $x^3-y^3=(x-y)(x^2+xy+y^2)$.

To Find:

We have to prove that Left hand side is equal to right hand side.

Step-by-step explanation:

• Whenever we need to prove Left hand side equal to right hand side we can take any of the side and then simplify that side to make it equal to the other side.

• Now we have the given equation which is written as

       $x^3-y^3=(x-y)(x^2+xy+y^2)$

• We will take the Right hand side

       $(x-y)(x^2+xy+y^2)$

• Now we opens the brackets by simply multiplying the each terms

        $x(x^2+xy+y^2)-y(x^2+xy+y^2)$

• Now further simplify them

        $x^3+x^2y+xy^2-yx^2-xy^2-y^3$

• Now take the like terms together and simplify them

       $x^3-y^3+x^2y-x^2y+xy^2-xy^2$

• Canceling the terms we get

       $x^3-y^3=L.H.S$

Hence, we get L.HS=R.HS