The area of room A is (5x2-7x-6) ft2. Room B has an area of (8x2+6x-1) ft2. If room A in the larger room, how much greater is the area of room A than the area of room B? Show your work.
A. -3x2-x-7
B. 13x2-13x-7
C. -3x2-13x-5
D. 3x2-x-5
To find the difference in area, we need to subtract the area of room B from the area of room A:
Area of A - Area of B = (5x^2 - 7x - 6) - (8x^2 + 6x - 1)
Simplifying by distributing the negative sign:
= 5x^2 - 7x - 6 - 8x^2 - 6x + 1
Combining like terms:
= -3x^2 - 13x - 5
Therefore, the answer is C. -3x^2 -13x -5, which represents the amount that room A is greater than room B in terms of area.