Answer:
![A(x) = 2x^2-22x+144](https://tex.z-dn.net/?f=A%28x%29%20%3D%202x%5E2-22x%2B144)
Step-by-step explanation:
We are given the following in the question:
Area of room =
![3x^2 + 2x](https://tex.z-dn.net/?f=3x%5E2%20%2B%202x)
Area of rug =
![x^2 + 24x - 144](https://tex.z-dn.net/?f=x%5E2%20%2B%2024x%20-%20144)
We have to find the area of of the room not covered by the rug.
Area of of the room not covered by the rug =
Area of room - Area of rug
![A(x)=(3x^2 + 2x) - ( x^2 + 24x - 144)\\A(x)=3x^2 + 2x-x^2 -24x + 144\\A(x)=(3x^2-x^2)+(2x -24x) + 144\\A(x)=2x^2-22x+144](https://tex.z-dn.net/?f=A%28x%29%3D%283x%5E2%20%2B%202x%29%20-%20%28%20x%5E2%20%2B%2024x%20-%20144%29%5C%5CA%28x%29%3D3x%5E2%20%2B%202x-x%5E2%20%20-24x%20%2B%20144%5C%5CA%28x%29%3D%283x%5E2-x%5E2%29%2B%282x%20-24x%29%20%2B%20144%5C%5CA%28x%29%3D2x%5E2-22x%2B144)
is the required expression for the area of floor not covered by the rug.
Answer:
true
Step-by-step explanation: