maths

the proof of the identity of the difference of two cubes is shown below:
L.H.S.=a^3-b^3
R.H.S.=(a-b)(a^2 + ab + b^2)
=a(a^2 + ab + b^2) - b(a^2 + ab + b^2)
=a^3 + a^2 b + ab^2 - ba^2 - ab^2 -b^3
=a^3 - b^3
L.H.S.=R.H.S.
so, a^3 - b^3 identity to (a-b)(a^2 + ab + b^2)

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

proof :
R.H.S=(x-y)(x^2+xy+y^2) <-----expend
=a^3 +a^2 b-a^2 b -ab^2+b^2 a +b^3
=a^3+b^3
=L.H.S