I ONLY NEED HELP WITH PART C I DID THE REST ON MY OWN plz help

Shane drew 3 squares with each side equal to n units. For each square, he does something different to it according to each part below.

Part A: Shane increased the length and width of the square by m units each. What will be the change in the area of the original square? Show your work. (4 points)

Part B: Shane decreased the length and width of the square by m units each. What will be the change in the area of the square? Show your work. (3 points)

Part C: Shane increased the length of the square by m units and decreased its width by m units. What will be the change in the area of the square? Show your work. (3 points)

Original square area = n*n u²

New dimensions: (n+m), (n-m)
New area = (n+m)(n-m)=n²-m² u²
Change in area = difference of above areas.

Chyttr

To find the change in the area of the square when the length is increased by m units and the width is decreased by m units, we can use the formula for the area of a square, which is side length squared.

Let's denote the original side length of the square as n units.

In Part A, Shane increased the length and width of the square by m units each, so the new side length will be (n + m) units.

The change in the area can be calculated by subtracting the original area from the new area:

Change in area = (n + m)^2 - n^2

Now, let's simplify the equation:
Change in area = (n^2 + 2nm + m^2) - n^2
Change in area = 2nm + m^2

Therefore, the change in the area of the original square in Part A is 2nm + m^2.

In Part B, Shane decreased the length and width of the square by m units each, so the new side length will be (n - m) units.

Using the same logic as in Part A, we can calculate the change in the area:
Change in area = (n - m)^2 - n^2
Change in area = (n^2 - 2nm + m^2) - n^2
Change in area = -2nm + m^2

Therefore, the change in the area of the square in Part B is -2nm + m^2.

Now, let's move to Part C, where Shane increased the length of the square by m units and decreased its width by m units.

The new length will be (n + m) units, and the new width will be (n - m) units.

To find the change in the area, we can calculate the new area and subtract the original area:

Change in area = (n + m) * (n - m) - n^2

Expanding the equation:
Change in area = (n^2 - m^2) - n^2
Change in area = -m^2

Therefore, the change in the area of the square in Part C is -m^2.

In summary, the changes in the areas for each part are:
Part A: 2nm + m^2
Part B: -2nm + m^2
Part C: -m^2