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

Question

Leonidas Sawyer

Mathematics

20 January, 06:56

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

+1

Answers (1)

Know the Answer?

Max Duffy · Answer 1

a^3 - b^3.

Step-by-step 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.