In a school project, João was invited to calculate the areas of several different squares, arranged in sequence, from left to right, as shown in the figure.
The first square in the sequence has a side measuring 1 cm, the second square has a side measuring 2 cm, the third square has a side measuring 3 cm, and so on. The objective of the project is to identify by how much the area of each square in the sequence exceeds the area of the previous square. The area of the square that occupies position $n$ in the sequence was represented by $\mathrm{A}_{n}$.
For $n \geq 2$, the value of the difference $\mathrm{A}_{n} - \mathrm{A}_{n-1}$, in square centimeter, is equal to
(A) $2n - 1$
(B) $2n + 1$
(C) $-2n + 1$
(D) $(n-1)^{2}$
(E) $n^{2} - 1$

What is the coefficient of $x$ in the expansion of $\left( 2 x + \frac { 1 } { 2 x } \right) ^ { 7 }$? [3 points]
(1) 14
(2) 28
(3) 42
(4) 56
(5) 70

In the expansion of $\left( x + \frac { 1 } { x ^ { 3 } } \right) ^ { 4 }$, what is the coefficient of $\frac { 1 } { x ^ { 4 } }$? [4 points]
(1) 4
(2) 6
(3) 8
(4) 10
(5) 12

In the expansion of $\left( x + \frac { 2 } { x } \right) ^ { 8 }$, find the coefficient of $x ^ { 4 }$. [3 points]
(1) 128
(2) 124
(3) 120
(4) 116
(5) 112

What is the coefficient of $x ^ { 4 }$ in the expansion of $\left( x + \frac { 2 } { x } \right) ^ { 8 }$? [3 points]
(1) 108
(2) 112
(3) 116
(4) 120
(5) 124

What is the coefficient of $x ^ { 4 }$ in the expansion of the polynomial $( 1 + x ) ^ { 7 }$? [3 points]
(1) 42
(2) 35
(3) 28
(4) 21
(5) 14

In the expansion of $\left( 2 x + \frac { 1 } { x ^ { 2 } } \right) ^ { 4 }$, what is the coefficient of $x$? [3 points]
(1) 16
(2) 20
(3) 24
(4) 28
(5) 32

Find the coefficient of $x$ in the expansion of $( 3 x + 1 ) ^ { 8 }$. [3 points]

Find the coefficient of $x ^ { 2 }$ in the expansion of $\left( x + \frac { 3 } { x ^ { 2 } } \right) ^ { 5 }$. [3 points]

In the expansion of the polynomial $( x + 2 ) ^ { 7 }$, what is the coefficient of $x ^ { 5 }$? [2 points]
(1) 42
(2) 56
(3) 70
(4) 84
(5) 98

What is the coefficient of $x ^ { 9 }$ in the expansion of $\left( x ^ { 3 } + 3 \right) ^ { 5 }$? [2 points]
(1) 30
(2) 60
(3) 90
(4) 120
(5) 150

What is the coefficient of $x^{6}$ in the expansion of $\left(x^{3} + 2\right)^{5}$? [2 points]
(1) 40
(2) 50
(3) 60
(4) 70
(5) 80

9. In the expansion of $( 2 + x ) ^ { 5 }$, the coefficient of $x ^ { 3 }$ is $\_\_\_\_$. (Answer with numerals)

12. The coefficient of $x ^ { 8 }$ in the expansion of $\left( x ^ { 3 } + \frac { 1 } { 2 \sqrt { x } } \right) ^ { 5 }$ is $\_\_\_\_$ (answer with numerals).

11. The coefficient of $x ^ { 2 }$ in the expansion of $( x + 2 ) ^ { 5 }$ equals $\_\_\_\_$. (Answer with a number)

11. In the expansion of $( 2 x - 1 ) ^ { 8 }$, the coefficient of the term containing $x^4$ is $\_\_\_\_$ (answer with a number).

In the expansion of $\left(x - \frac{1}{4x}\right)^6$, the coefficient of $x^2$ is .