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??
First, we need to find the area of the entire wall before the mural is painted.
Area of the wall before the mural = (6x + 7)(8x + 5)
Expanding this expression, we get:
Area of the wall before the mural = 48x^2 + 30x + 56x + 35
Area of the wall before the mural = 48x^2 + 86x + 35
Next, let's find the area of the mural itself.
Area of the mural = (x + 4)(2x + 5)
Expanding this expression, we get:
Area of the mural = 2x^2 + 5x + 8x + 20
Area of the mural = 2x^2 + 13x + 20
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 wall before the mural:
Area of remaining wall = (48x^2 + 86x + 35) - (2x^2 + 13x + 20)
Area of remaining wall = 48x^2 + 86x + 35 - 2x^2 - 13x - 20
Area of remaining wall = 46x^2 + 73x + 15
Therefore, the area of the remaining wall after the mural has been painted is 46x^2 + 73x + 15.