Question

The length and breath of a rectangle are (a^2 +ab +b^2) units and (a-b) units.Find the area of the rectangle.

Answer 1

a^3 - b^3.

Explanation:

Area = length * breadth

= (a - b)(a^2 + ab + b^2)

= a(a^2 + ab + b^2) - b(a^2 + ab + b^2)

= a^3 + a^2b + ab^2 - a^2b - ab^2 - b^3

Note: the 4 middle terms cancel out. So the answer is

a^3 - b^3.