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??

Answer 1

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.