HCF and LCM of two numbers p and q is A and B respectively, if A + B = p + q, then the value of A3 + B3 is:

p3 + q3 q3 p3 p3 − q3

p3 + q3

L.C.M × H.C.F = product of numbers So, A × B = p × q      ----(i) And, it is given that A + B = p + q      ----(ii) we know, A3 + B3 = (A + B)[(A + B)2 – 3AB] ⇒ A3 + B3 = p + q [(p + q)2 – 3pq] ∴ A3 + B3 = p3 + q3