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.