Question

If a-b=1 prove that a^3+b^3=(a+b)(1+ab)

Answer 1

given ,
a-b=1

LHS=a^3+b^3
=(a+b)(a^2+b^2-ab) -----------(1)

now,
a-b=1
take square both side
a^2+b^2-2ab=1
add both side ab
a^2+b^2-ab=1+ab
put this equation (1)
now ,
LHS=(a+b)(1+ab)=RHS

Answer 2

HENCE PROVED ...............................