A wall with an area of (3x2 + 4x + 1) square units has a rectangular window that has a width of (x + 2) units and a length of (x + 1) units. The wall also has a built - in shelving unit that occupies an area of (x2 + 5x + 6) square units of wall space. If the wall is to be covered with wallpaper, how much wallpaper will be required?

The question seems to ask available area and not how much wallpaper is required. Let's calculate the area of the rectangular window. Area of a rectangle = Length * Breath Area = (x + 2) * (x + 1) = x^2 + 3x + 2 The wall also has a built - in shelving unit that occupies an area of (x^2 + 5x + 6). So total area occupied by the rectangular wall and shelf is (x^2 + 3x + 2) + (x^2 + 5x + 6) = 2x^2 + 8x + 8. If the wall is to be covered with wallpaper, the total available area = (3x^2 + 4x + 1) - (2x^2 + 8x + 8) = x^2 - 4x - 7