The formula for determining the area of a rectangle is expressed as
Area = length x width
Given that
length = 2x + 10
width = 50 - x
The area would be
Area = (2x + 10)(50 - x)
We would open the bracket by multiplying the terms inside one bracket by the terms inside the second bracket. Thus, we have
Area = 2x * 50 + 2x * - x + 10 * 50 + 10 * - x
Area = 100x - 2x^2 + 500 - 10x
Area = - 2x^2 + 100x - 10x + 500
Area = - 2x^2 + 90x + 500
The expression for the area is
- 2x^2 + 90x + 500
