Answer:
Area of gray region = [tex]8x^2+8x-7[/tex]
Step-by-step explanation:
The area covered by the furniture can be subtracted from the total area of the room to calculate the area of the gray region.
Total area of the room: [tex]13x^2+7x-2[/tex]
Area taken up by furniture: [tex]5x^2-x+5[/tex]
Area of gray region = total area of the room - area taken up by furniture
Area of gray region = [tex]13x^2+7x-2-(5x^2-x+5)[/tex]
Remember to distribute the negative sign:
Area of gray region = [tex]13x^2+7x-2-5x^2+x-5[/tex]
Combine like terms:
Area of gray region = [tex]8x^2+8x-7[/tex]
