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?
To find the area of the remaining wall after the mural has been painted, we first need to calculate the area of the mural.
Area of the mural = (x+4) * (2x+5)
= 2x^2 + 8x + 5x + 20
= 2x^2 + 13x + 20
Now, we calculate the area of the entire wall:
Area of the entire wall = (6x+7) * (8x+5)
= 48x^2 + 40x + 56x + 35
= 48x^2 + 96x + 35
Finally, we find the area of the remaining wall:
Area of remaining wall = Area of the entire wall - Area of the mural
= 48x^2 + 96x + 35 - (2x^2 + 13x + 20)
= 48x^2 + 96x + 35 - 2x^2 - 13x - 20
= 46x^2 + 83x + 15
Therefore, the area of the remaining wall after the mural has been painted is 46x^2 + 83x + 15.