A group of art students are painting a mural on a wall. The rectangular wall has dimensions of (6x + 7) by (8x + 5) and they are planing the mural to be (x + 4) by (2x + 5). What is the area of the remaining wall after the mural has been painted?
(1 point)
A. 46x^2 + 73x + 15
B. 48x^2 + 86x + 35
C. 2x^2 + 13x + 20
D. 50x^2 + 99x + 55
The area of the wall before the mural is painted is given by the product of the dimensions (6x+7) and (8x+5):
Area of the wall = (6x + 7)(8x + 5)
The area of the mural is given by the product of its dimensions (x+4) and (2x+5):
Area of the mural = (x + 4)(2x + 5)
To find the area of the remaining wall after the mural has been painted, we subtract the area of the mural from the area of the wall:
Remaining area = Area of the wall - Area of the mural
Remaining area = (6x + 7)(8x + 5) - (x + 4)(2x + 5)
Expanding both products:
Remaining area = 48x^2 + 30x + 42x + 35 - 2x^2 - 10x + 10x + 20
Combining like terms:
Remaining area = 46x^2 + 74x + 55 - 2x^2
Simplifying:
Remaining area = 44x^2 + 74x + 55
Therefore, the area of the remaining wall after the mural has been painted is 44x^2 + 74x + 55.
The correct option is D. 50x^2 + 99x + 55 is not correct because the coefficient of x^2 differs from the obtained expression.