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

Mathematics

Laura

29 December, 01:23

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

+4

Answers (1)

Know the Answer?

Maddison Miles · 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.