The area of room A is (5x^2 – 7x – 6) ft^2. Room B has an area of (8x^2 + 6x – 1) ft^2. If room A is the larger room, how much greater is the area of room A than the area of room B?
(1 point)
Responses
–3x^2 – x – 7
13x^2 – 13x – 7
–3x^2 – 13x – 5
3x%2 – x – 5
13x^2 - 13x - 7
The area of room A is 5x^2 - 7x - 6 = 5x^2 - 15x + 8x - 6 = (5x - 3)(x + 2)
The area of room B is 8x^2 + 6x - 1 = 8x^2 - 4x + 10x - 1 = (4x - 1)(2x + 1)
To find how much greater the area of room A is than the area of room B, we will find the difference of the two areas:
(5x - 3)(x + 2) - (4x - 1)(2x + 1)
= 5x^2 + 10x - 3x - 6 - (8x^2 + 4x - 2x - 1)
= 5x^2 + 7x - 6 - 8x^2 - 2x + 1
= -3x^2 + 5x - 5
= 13x^2 - 13x - 7
Therefore, the area of room A is 13x^2 - 13x - 7 greater than the area of room B.