A carpenter is putting a skylight in a roof. If the roof measures 10x + 8 by 8x + 6 and the skylight measures x + 5 by 3x + 4, what is the area of the remaining roof after the skylight is built?
First, we need to find the area of the entire roof.
Area of the entire roof = (10x + 8) * (8x + 6)
= 80x^2 + 52x + 48x + 48
= 80x^2 + 100x + 48
Next, we need to find the area of the skylight.
Area of the skylight = (x + 5) * (3x + 4)
= 3x^2 + 4x + 15x + 20
= 3x^2 + 19x + 20
Now, to find the area of the remaining roof after the skylight is built, we need to subtract the area of the skylight from the area of the entire roof.
Area of the remaining roof = Area of the entire roof - Area of the skylight
= 80x^2 + 100x + 48 - (3x^2 + 19x + 20)
= 80x^2 + 100x + 48 - 3x^2 - 19x - 20
= 77x^2 + 81x + 28
Therefore, the area of the remaining roof after the skylight is built is 77x^2 + 81x + 28.