A group of art students are painting a mural on a wall. The rectangular 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? 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
To find the area of the remaining wall after the mural has been painted, we first need to find the area of the mural, and then subtract it from the area of the initial wall.
Area of the mural = (x + 4)(2x + 5)
Expand: Area of the mural = 2x^2 + 5x + 8x + 20
Area of the mural = 2x^2 + 13x + 20
Now, to find the area of the initial wall, we multiply the length and width:
Area of the initial wall = (6x + 7)(8x + 5)
Expand: Area of the initial wall = 6x*8x + 6x*5 + 7*8x + 7*5
Area of the initial wall = 48x^2 + 30x + 56x + 35
Area of the initial wall = 48x^2 + 86x + 35
Now, 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 initial wall:
Remaining wall area = Area of the initial wall - Area of the mural
Remaining wall area = (48x^2 + 86x + 35) - (2x^2 + 13x + 20)
Remaining wall area = 46x^2 + 73x + 15
Therefore, the area of the remaining wall after the mural has been painted is 46x^2 + 73x + 15.