Math worksheet for practicing collecting like terms in algebraic expressions.

Problem: Collecting Like Terms

The task involves simplifying algebraic expressions by collecting like terms. Like terms are terms that have the same variable(s) raised to the same power(s). For example, in the expression \(3a - a\), both terms involve the variable \(a\), so they can be combined.

#### Question Set 1:

1. \(3b - 2b = \)
- Both terms involve the variable \(b\).
- Combine the coefficients: \(3 - 2 = 1\).
- Simplified expression: \(b\).

Answer: \(b\)

2. \(4c - 2c = \)
- Both terms involve the variable \(c\).
- Combine the coefficients: \(4 - 2 = 2\).
- Simplified expression: \(2c\).

Answer: \(2c\)

3. \(2d + 4d - 3d = \)
- All terms involve the variable \(d\).
- Combine the coefficients: \(2 + 4 - 3 = 3\).
- Simplified expression: \(3d\).

Answer: \(3d\)

4. \(7a + 2a - a = \)
- All terms involve the variable \(a\).
- Combine the coefficients: \(7 + 2 - 1 = 8\).
- Simplified expression: \(8a\).

Answer: \(8a\)

5. \(3f + 5f - 3f = \)
- All terms involve the variable \(f\).
- Combine the coefficients: \(3 + 5 - 3 = 5\).
- Simplified expression: \(5f\).

Answer: \(5f\)

6. \(-4g + 7g = \)
- Both terms involve the variable \(g\).
- Combine the coefficients: \(-4 + 7 = 3\).
- Simplified expression: \(3g\).

Answer: \(3g\)

7. \(7h - 9h + 3h - 2h = \)
- All terms involve the variable \(h\).
- Combine the coefficients: \(7 - 9 + 3 - 2 = -1\).
- Simplified expression: \(-h\).

Answer: \(-h\)

8. \(-i - 6i + 2i + 3i = \)
- All terms involve the variable \(i\).
- Combine the coefficients: \(-1 - 6 + 2 + 3 = -2\).
- Simplified expression: \(-2i\).

Answer: \(-2i\)

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#### Question Set 2:

1. \(4j - 7j + 6k - 2k = \)
- Combine the \(j\) terms: \(4j - 7j = -3j\).
- Combine the \(k\) terms: \(6k - 2k = 4k\).
- Simplified expression: \(-3j + 4k\).

Answer: \(-3j + 4k\)

2. \(8m - 3m - 2n + 6n = \)
- Combine the \(m\) terms: \(8m - 3m = 5m\).
- Combine the \(n\) terms: \(-2n + 6n = 4n\).
- Simplified expression: \(5m + 4n\).

Answer: \(5m + 4n\)

3. \(6p + p - 4r + 8r = \)
- Combine the \(p\) terms: \(6p + p = 7p\).
- Combine the \(r\) terms: \(-4r + 8r = 4r\).
- Simplified expression: \(7p + 4r\).

Answer: \(7p + 4r\)

4. \(-5x + 2x + 15x - 12x = \)
- Combine all \(x\) terms: \(-5x + 2x + 15x - 12x = 0\).
- Simplified expression: \(0\).

Answer: \(0\)

5. \(t + 5t - 3u + u = \)
- Combine the \(t\) terms: \(t + 5t = 6t\).
- Combine the \(u\) terms: \(-3u + u = -2u\).
- Simplified expression: \(6t - 2u\).

Answer: \(6t - 2u\)

6. \(-7v + 6v - 4v + 5v = \)
- Combine all \(v\) terms: \(-7v + 6v - 4v + 5v = 0\).
- Simplified expression: \(0\).

Answer: \(0\)

7. \(7w - 2w + 7w - 2w = \)
- Combine all \(w\) terms: \(7w - 2w + 7w - 2w = 10w\).
- Simplified expression: \(10w\).

Answer: \(10w\)

8. \(11a + 8b - a - 19b - 4a = \)
- Combine the \(a\) terms: \(11a - a - 4a = 6a\).
- Combine the \(b\) terms: \(8b - 19b = -11b\).
- Simplified expression: \(6a - 11b\).

Answer: \(6a - 11b\)

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Final Answers:

Question Set 1:
1. \(b\)
2. \(2c\)
3. \(3d\)
4. \(8a\)
5. \(5f\)
6. \(3g\)
7. \(-h\)
8. \(-2i\)

Question Set 2:
1. \(-3j + 4k\)
2. \(5m + 4n\)
3. \(7p + 4r\)
4. \(0\)
5. \(6t - 2u\)
6. \(0\)
7. \(10w\)
8. \(6a - 11b\)

Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
\text{Question Set 1:} & \text{Question Set 2:} \\
1. b & 1. -3j + 4k \\
2. 2c & 2. 5m + 4n \\
3. 3d & 3. 7p + 4r \\
4. 8a & 4. 0 \\
5. 5f & 5. 6t - 2u \\
6. 3g & 6. 0 \\
7. -h & 7. 10w \\
8. -2i & 8. 6a - 11b \\
\end{array}
}
\]