Answer:No
Step-by-step explanation:
The negative in front of the second bracket means that it's times by -1 so each of their signs switches:
3m^2+2n-m^2-2n
Add like terms
2m^2
the 2n cancels out
Answer:

Step-by-step explanation:
From the image attached below;
We need to calculate the limits of x and y to find the double integral
We will notice that y varies from 1 to 2
The line equation for (0,1),(1,2) is:

y - 1 = x
The line equtaion for (1,2),(4,1) is:

-3(y-2) = (x -1)
-3y + 6 = x - 1
-x = 3y - 6 - 1
-x = 3y - 7
x = -3y + 7
This implies that x varies from y - 1 to -3y + 7
Now, the region D = {(x,y) | 1 ≤ y ≤ 2, y - 1 ≤ x ≤ -3y + 7}
The double integral can now be calculated as:

![\iint _D y^2 dA= \int ^2_1 \bigg[ 2xy ^2 \bigg]^{-3y+7}_{y-1} \ dy](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%5Cint%20%5E2_1%20%5Cbigg%5B%202xy%20%5E2%20%5Cbigg%5D%5E%7B-3y%2B7%7D_%7By-1%7D%20%20%5C%20dy)
![\iint _D y^2 dA= \int ^2_1 \bigg[2(-3y+7)y^2-2(y-1)y^2 \bigg ] \ dy](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%5Cint%20%5E2_1%20%5Cbigg%5B2%28-3y%2B7%29y%5E2-2%28y-1%29y%5E2%20%5Cbigg%20%5D%20%20%5C%20dy)
![\iint _D y^2 dA= \int ^2_1 \bigg[-6y^3 +14y^2 -2y^3 +2y^2 \bigg ] \ dy](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%5Cint%20%5E2_1%20%5Cbigg%5B-6y%5E3%20%2B14y%5E2%20-2y%5E3%20%2B2y%5E2%20%5Cbigg%20%5D%20%20%5C%20dy)
![\iint _D y^2 dA= \int ^2_1 \bigg[-8y^3 +16y^2 \bigg ] \ dy](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%5Cint%20%5E2_1%20%5Cbigg%5B-8y%5E3%20%2B16y%5E2%20%20%5Cbigg%20%5D%20%20%5C%20dy)
![\iint _D y^2 dA= \bigg[-8(\dfrac{y^4}{4}) +16(\dfrac{y^3}{3})\bigg ] ^2_1](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%20%5Cbigg%5B-8%28%5Cdfrac%7By%5E4%7D%7B4%7D%29%20%20%2B16%28%5Cdfrac%7By%5E3%7D%7B3%7D%29%5Cbigg%20%5D%20%5E2_1)
![\iint _D y^2 dA= \bigg[-8(\dfrac{16}{4}-\dfrac{1}{4}) +16(\dfrac{8}{3}-\dfrac{1}{3})\bigg ]](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%20%5Cbigg%5B-8%28%5Cdfrac%7B16%7D%7B4%7D-%5Cdfrac%7B1%7D%7B4%7D%29%20%20%2B16%28%5Cdfrac%7B8%7D%7B3%7D-%5Cdfrac%7B1%7D%7B3%7D%29%5Cbigg%20%5D)
![\iint _D y^2 dA= \bigg[-8(\dfrac{15}{4}) +16(\dfrac{7}{3})\bigg ]](https://tex.z-dn.net/?f=%5Ciint%20_D%20y%5E2%20dA%3D%20%20%5Cbigg%5B-8%28%5Cdfrac%7B15%7D%7B4%7D%29%20%20%2B16%28%5Cdfrac%7B7%7D%7B3%7D%29%5Cbigg%20%5D)



12 feet times 14 feet gives us the AREA of the room, not the PERIMETER. No soap.