The area of room A is (5x2 – 7x – 6) ft2. Room B has an area of (8x2 + 6x – 1) ft2. If room A is the larger room, how much greater is the area of room A than the area of room B?
A. –3x2 – x – 7
B. 13x2 – 13x – 7
C. –3x2 – 13x – 5
D. 3x2 – x – 5
To find the difference between the two areas, we need to subtract the area of room B from the area of room A.
(5x^2 - 7x - 6) - (8x^2 + 6x - 1)
Simplifying the expression by distributing the negative sign, we get:
5x^2 - 7x - 6 - 8x^2 - 6x + 1
Combining like terms, we get:
-3x^2 - 13x - 5
Therefore, the answer is option C: –3x2 – 13x – 5.
To find the difference in area between room A and room B, we need to subtract the area of room B from the area of room A.
The area of room A is given as (5x^2 - 7x - 6) ft^2.
The area of room B is given as (8x^2 + 6x - 1) ft^2.
To find the difference, we subtract the area of room B from the area of room A:
(5x^2 - 7x - 6) - (8x^2 + 6x - 1)
= 5x^2 - 7x - 6 - 8x^2 - 6x + 1
= (5x^2 - 8x^2) + (-7x - 6x) + (-6 + 1)
= -3x^2 - 13x - 5
Therefore, the correct answer is C. -3x^2 - 13x - 5.
To calculate the difference in area between room A and room B, we need to subtract the area of room B from the area of room A.
Area of room A = 5x^2 – 7x – 6 ft^2
Area of room B = 8x^2 + 6x – 1 ft^2
To find the difference, we subtract the area of room B from the area of room A:
Difference = (5x^2 – 7x – 6) - (8x^2 + 6x – 1)
To subtract these polynomials, we combine like terms. In this case, we combine the x^2 terms, the x terms, and the constant terms:
Difference = (5x^2 – 8x^2) + (-7x – 6x) + (-6 – (-1))
Simplifying further, we get:
Difference = -3x^2 – 13x – 5
Therefore, the area of room A is greater than the area of room B by: -3x^2 – 13x – 5.
Hence, the correct answer choice is C. -3x^2 – 13x – 5.