Algebra quiz worksheet with 12 multiple-choice questions on simplifying algebraic expressions.

Problem Analysis

The task involves simplifying algebraic expressions and identifying the correct simplified forms. Let's solve each problem step by step.

---

Question 1:

Expression: \( 4x + 2y - 6 \)

Task: Identify the variables in the expression.

- The variables in the expression are \( x \) and \( y \).

Correct Answer:
A. X and Y

---

Question 2:

Expression: \( -7p - 8q + p - q \)

Task: Simplify the expression.

1. Group like terms:
- Terms involving \( p \): \( -7p + p = -6p \)
- Terms involving \( q \): \( -8q - q = -9q \)

2. Combine the results:
\[
-7p - 8q + p - q = -6p - 9q
\]

Correct Answer:
A. -6p - 9q

---

Question 3:

Expression: \( 3k - 3xy - 5xy + 2k \)

Task: Simplify the expression.

1. Group like terms:
- Terms involving \( k \): \( 3k + 2k = 5k \)
- Terms involving \( xy \): \( -3xy - 5xy = -8xy \)

2. Combine the results:
\[
3k - 3xy - 5xy + 2k = 5k - 8xy
\]

Correct Answer:
C. 5k - 8xy

---

Question 4:

Expression: \( 2bc + 10 - 3bc - 2 \)

Task: Simplify the expression.

1. Group like terms:
- Terms involving \( bc \): \( 2bc - 3bc = -bc \)
- Constant terms: \( 10 - 2 = 8 \)

2. Combine the results:
\[
2bc + 10 - 3bc - 2 = -bc + 8
\]

Correct Answer:
D. 8 - bc

---

Question 5:

Expression: \( c - 2d + cd - 10cd - d + 4c \)

Task: Simplify the expression.

1. Group like terms:
- Terms involving \( c \): \( c + 4c = 5c \)
- Terms involving \( d \): \( -2d - d = -3d \)
- Terms involving \( cd \): \( cd - 10cd = -9cd \)

2. Combine the results:
\[
c - 2d + cd - 10cd - d + 4c = 5c - 3d - 9cd
\]

Correct Answer:
C. 5c - 3d - 9cd

---

Question 6:

Expression: \( 12mn - 4p - 6 + 7p \)

Task: Simplify the expression.

1. Group like terms:
- Terms involving \( mn \): \( 12mn \) (no other \( mn \)-terms)
- Terms involving \( p \): \( -4p + 7p = 3p \)
- Constant term: \( -6 \) (no other constant terms)

2. Combine the results:
\[
12mn - 4p - 6 + 7p = 12mn + 3p - 6
\]

Correct Answer:
D. 12mn + 3p - 6

---

Question 7:

Expression: \( -9 - rs + 9rs + 9 \)

Task: Simplify the expression.

1. Group like terms:
- Terms involving \( rs \): \( -rs + 9rs = 8rs \)
- Constant terms: \( -9 + 9 = 0 \)

2. Combine the results:
\[
-9 - rs + 9rs + 9 = 8rs
\]

Correct Answer:
B. 8rs

---

Final Answers:

1. A. X and Y
2. A. -6p - 9q
3. C. 5k - 8xy
4. D. 8 - bc
5. C. 5c - 3d - 9cd
6. D. 12mn + 3p - 6
7. B. 8rs

\boxed{A, A, C, D, C, D, B}