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The image contains a list of algebraic expressions that need to be simplified. Here’s how we can approach the first few problems in the list.

### 1. Simplify the following algebraic expressions:

#### Expression (a):
\[
3x^2 - 2x^2 + x - 5x - 2
\]
**Step-by-step simplification**:
- Combine like terms involving \(x^2\): \(3x^2 - 2x^2 = x^2\)
- Combine like terms involving \(x\): \(x - 5x = -4x\)
- The constant term is \(-2\).

So, the simplified expression is:
\[
x^2 - 4x - 2
\]

#### Expression (b):
\[
10e + 3f - 2e - (-5f)
\]
**Step-by-step simplification**:
- Combine like terms involving \(e\): \(10e - 2e = 8e\)
- Combine like terms involving \(f\): \(3f - (-5f) = 3f + 5f = 8f\)

So, the simplified expression is:
\[
8e + 8f
\]

#### Expression (c):
\[
6ab - 5cd + 8ba - 2dc
\]
**Step-by-step simplification**:
- Recognize that \(ab = ba\) and \(cd = dc\), so we can combine these terms:
- Combine like terms involving \(ab\): \(6ab + 8ba = 14ab\)
- Combine like terms involving \(cd\): \(-5cd - 2dc = -7cd\)

So, the simplified expression is:
\[
14ab - 7cd
\]

#### Expression (d):
\[
3lm - 4ml + 3l - 2m
\]
**Step-by-step simplification**:
- Recognize that \(lm = ml\), so the terms \(3lm\) and \(-4ml\) can be combined:
- Combine like terms involving \(lm\): \(3lm - 4ml = -lm\)
- The remaining terms are \(3l\) and \(-2m\), which cannot be simplified further.

So, the simplified expression is:
\[
-lm + 3l - 2m
\]

#### Expression (e):
\[
5x^2 - 4x^2 + x + (-5x) - 2
\]
**Step-by-step simplification**:
- Combine like terms involving \(x^2\): \(5x^2 - 4x^2 = x^2\)
- Combine like terms involving \(x\): \(x - 5x = -4x\)
- The constant term is \(-2\).

So, the simplified expression is:
\[
x^2 - 4x - 2
\]

Let me know if you'd like more details or explanations for any specific parts of these solutions!

### Related questions:
1. How do you handle subtraction of negative terms when simplifying expressions?
2. What are like terms, and why are they important in simplification?
3. Can two terms like \(ab\) and \(ba\) always be combined?
4. How do you combine terms involving exponents in algebraic expressions?
5. What are common mistakes to avoid when simplifying algebraic expressions?

**Tip**: When simplifying, always group similar terms (same variable and exponent) to avoid errors.

Simplify the following algebraic expressions from the list in the image: (a) 3x^2 - 2x^2 + x - 5x - 2, (b) 10e + 3f - 2e - (-5f), (c) 6ab - 5cd + 8ba - 2dc.

Learn how to simplify algebraic expressions by combining like terms in problems such as 3x^2 - 2x^2 + x - 5x - 2. This guide covers key concepts like combining like terms, recognizing patterns, and simplifying expressions. Ideal for Grades 7-9 students.

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