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?

Question

(1 point)
Responses

–3x^2 – x – 7

13x^2 – 13x – 7

–3x^2 – 13x – 5

3x^2 – x – 5

Answer 1

To find the difference in area between room A and room B, we can subtract the area of room B from the area of room A:

Area of room A - Area of room B
= (5x^2 – 7x – 6) - (8x^2 + 6x – 1)
= 5x^2 – 7x – 6 - 8x^2 - 6x + 1
= -3x^2 - 13x - 5

Therefore, the area of room A is 3x^2 - x - 5 greater than the area of room B. The correct answer is:

3x^2 - x - 5.