Question

Urgent ;if a^3+b^3=11 and a^3-b^3=5, evaluate a^6-b^6

Answer 1

Factorize using the difference of squares identity.

$a^6 - b^6 = \left(a^3\right)^2 - \left(b^3\right)^2 = \left(a^3 - b^3\right) \left(a^3 + b^3\right)$

Then

$a^6 - b^6 = 11 \cdot 5 = \boxed{55}$