The dimensions of the rectangular deck are (5x + 2) wide by (3x + 1) long.
The area of the deck is
A₁ = (5x + 2)(3x + 1)
= 15x² + 5x + 6x + 2
= 15x² + 11x + 2
Answer: 15x² + 11x + 2
The dimensions of the spa are (2x + 3) wide by (x + 2) long.
The area of the spa is
A₂ = (2x + 3)(x + 2)
= 2x² + 4x + 3x + 6
= 2x² + 7x + 6
Answer: 2x² + 7x + 6
The area remaining after the hole for the spa has been cut from the deck(the area of the new deck) is
A = A₁ - A₂
= 15x² + 11x + 2 - (2x² + 7x + 6)
= 15x² - 2x² + 11x - 7x + 2 - 6
= 13x² + 9x - 4
Answer: 13x² + 9x - 4
If x = 2 feet, the area of the new deck is
A(2) = 13*2² + 9*2 - 4 = 78 ft²
Answer: 78 ft²
