### Instruction: You have a square that has a side length of $1$ centimeter. Each minute, $2$ centimeters are added to the side length. After $10$ minutes, what will be the difference between the area of the last square and the area of the initial square in square centimeters (do not include the units in your answer)?### Response: I know that the area of a square is given by the formula $A = s^2$, where $s$ is the side length.
So, to find the area of the initial square, I just plug in $s = 1$ and get $A = 1^2 = 1$ square centimeter.
To find the area of the last square, I need to know what the side length is after $10$ minutes.
I notice that each minute, the side length increases by $2$ centimeters, so after $10$ minutes, it will increase by $2 \times 10 = 20$ centimeters.
That means the side length of the last square is $1 + 20 = 21$ centimeters.
Plugging that into the formula, I get $A = 21^2 = 441$ square centimeters.