Answer:
The area is: [tex]77x^2 + 105x + 28[/tex], option b.
Step-by-step explanation:
Rectangular area:
The area of a rectangular space is given bt the multiplication of its measures.
Area of the roof:
Dimensions of 10x + 8 and 8x + 6. So
[tex]A_{r} = (10x+8)(8x+6) = 80x^2 + 60x + 64x + 48 = 80x^2 + 124x + 48[/tex]
Area of the skylight:
Dimensions of x + 5 and 3x + 4. So
[tex]A_{s} = (x+5)(3x+4) = 3x^2+4x+15x+20 = 3x^2 + 19x + 20[/tex]
What is the area of the remaining roof after the skylight is built?
Total subtracted by the skylight, which is a subtraction of a polynomial, in which we subtract the like terms. So
[tex]A_{r} - A_{s} = 80x^2 + 124x + 48 - (3x^2 + 19x + 20) = 80x^2 - 3x^2 + 124x - 19x + 48 - 20 = 77x^2 + 105x + 28[/tex]
The area is: [tex]77x^2 + 105x + 28[/tex], option b.
