Question

Verify x^3-y^3=x^2+xy+y^2

Answer 1

Answer:

R.H.S => (x+y) ( x2 - xy + y2)

=> x3 - x2y + xy2 + x2y - xy2 + y3              

{On multiplying x3 + y3 with (x+y) ( x2 - xy + y2)}

=> [x3 + y3] + ( -x2y + x2y) + ( xy2 - xy2)

=>  x3 + y3

Since R.H.S = L.H.S,

That is x3 + y3 = x3 + y3

Hence, verified that

x3 + y3 = (x+y) ( x2 - xy + y2)