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?
To find the area of the remaining wall, we first need to calculate the area of the entire wall and then subtract the area of the mural.
The area of the entire wall is given by:
Area of wall = length * width
Area of wall = (6x + 7) * (8x + 5)
The area of the mural is given by:
Area of mural = length * width
Area of mural = (x + 4) * (2x + 5)
Now we can find the area of the remaining wall by subtracting the area of the mural from the area of the entire wall:
Remaining wall area = (6x + 7) * (8x + 5) - (x + 4) * (2x + 5)
Remaining wall area = 48x^2 + 30x + 56x + 35 - 2x^2 - 5x + 8x + 20
Remaining wall area = 46x^2 + 89x + 35 - 2x^2 + 3x + 20
Remaining wall area = 44x^2 + 92x + 55
Therefore, the area of the remaining wall after the mural has been painted is 44x^2 + 92x + 55.