Question

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

Answer 1

Answer:

Proving

        x3−y3=(x−y)(x2+xy+y2)

Step-by-step explanation:

We know that

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

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

(x+y)^3=x^3+y^3=(x+y)[(x+y)^2-3xy]                  ( taking (x+y) common )

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

(x+y)^3=(x−y)(x2+xy+y2)

LHS=RHS

Hence proved