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 planning 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)
Responses
46x2 + 73x + 15
46 x 2 + 73 x + 15
48x2 + 86x + 35
48 x 2 + 86 x + 35
2x2 + 13x + 20
2 x 2 + 13 x + 20
50x2 + 99x + 55
50 x 2 + 99 x + 55
The area of the remaining wall after the mural has been painted can be calculated by finding the total area of the wall and subtracting the area of the mural.
Total area of the wall = (6x + 7)(8x + 5) = 48x^2 + 30x + 56x + 35 = 48x^2 + 86x + 35
Area of the mural = (x + 4)(2x + 5) = 2x^2 + 10x + 4x + 20 = 2x^2 + 14x + 20
Remaining area = Total area - Area of the mural
Remaining area = 48x^2 + 86x + 35 - 2x^2 - 14x - 20
Remaining area = 46x^2 + 72x + 15
Therefore, the correct answer is:
46x^2 + 72x + 15