Question

The area of a rectangle is expressed as 81x²−4y² square units. Determine the dimensions of the rectangle by factoring the area expression completely.

A) (9x+2y)(9x−2y)
B) (9x+2y)2
C) (9x−2y)2
D) (9x+2y)(9x+2y)

Answer 1

The dimensions of the rectangle, factored using the difference of squares formula, are (9x+2y) and (9x−2y).

Step-by-step explanation:

The area of a rectangle is given by the expression 81x²−4y². To determine the dimensions of the rectangle, we need to factor the area expression completely. Using the difference of squares formula, we can rewrite 81x²−4y² as (9x+2y)(9x−2y). Therefore, the dimensions of the rectangle are (9x+2y) and (9x−2y).