Question

to prove x³-y³=(x-y)(x²+xy+y²)​

Answer 1

Step-by-step explanation:

(X-Y)³ = X³-Y³-3XY(X-Y)

keeping x³ and y³ on one side move remaining value on R.H.S to other side

Now,

X³-Y³= (X-Y)³+3XY (X-Y)

take (X-Y) as common out from RHS

X³-Y³ = (X-Y) ((X-Y)²+3XY)

Expand (X-Y)²

X³-Y³= (X-Y) ((X²+Y²-2XY+3XY)

X³-Y³= (X-Y)(X²+Y²+XY)

thus proved.