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?

Answer 1

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.