Answer:
Area of gray region =
![8x^2+8x-7](https://img.qammunity.org/2022/formulas/mathematics/high-school/mc9cgyv11qr424y9p7lcil2406ri5g8myc.png)
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:
![13x^2+7x-2](https://img.qammunity.org/2022/formulas/mathematics/high-school/2bfkvr2mbxgb229bs0xe6whf8d7guj54mq.png)
Area taken up by furniture:
![5x^2-x+5](https://img.qammunity.org/2022/formulas/mathematics/high-school/27fh0o5vbv0akmbp8xyjakobgabgmbnij4.png)
Area of gray region = total area of the room - area taken up by furniture
Area of gray region =
![13x^2+7x-2-(5x^2-x+5)](https://img.qammunity.org/2022/formulas/mathematics/high-school/34f2nibfl65eqsuy954z8xmqjdaf2h52ad.png)
Remember to distribute the negative sign:
Area of gray region =
![13x^2+7x-2-5x^2+x-5](https://img.qammunity.org/2022/formulas/mathematics/high-school/3x2wmhgyknsndnni50jaxhvi9hwj66itns.png)
Combine like terms:
Area of gray region =
![8x^2+8x-7](https://img.qammunity.org/2022/formulas/mathematics/high-school/mc9cgyv11qr424y9p7lcil2406ri5g8myc.png)