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I can assist with solving the problems from the image you uploaded. I'll go through each question one by one and provide detailed solutions. Let's begin:

### Problem 13:
\[ 192x^2y + 72x^3 - 24rxy - 9x^2 \]

**Step 1**: Group similar terms. This expression has terms with \(x^2y\), \(x^3\), \(rxy\), and a constant multiplied by \(x^2\).
So, no like terms can be simplified further in this case.

This expression doesn't factor neatly as it's already in its simplest form. No common factor across all terms.

### Problem 14:
\[ 90au - 36av - 150yu + 60yu \]

**Step 1**: Simplify by combining like terms. 

- Combine terms involving \( yu \): \( -150yu + 60yu = -90yu \)
  
So, the simplified expression is:
\[ 90au - 36av - 90yu \]

### Problem 15:
\[ 140ab - 60a^2 + 168b - 72a \]

**Step 1**: Check for common factors.

- Group similar terms to see if any factoring is possible.
\[ = (140ab - 60a^2) + (168b - 72a) \]
  
- Factor out common terms:
\[ = 20a(7b - 3a) + 24(7b - 3a) \]

- Now factor the expression:
\[ = (7b - 3a)(20a + 24) \]

### Problem 16:
\[ 105ab - 90a - 21b + 18 \]

**Step 1**: Try grouping terms and factoring.

- Group similar terms:
\[ = (105ab - 90a) - (21b - 18) \]

- Factor out common terms:
\[ = 15a(7b - 6) - 3(7b - 6) \]

- Factor further:
\[ = (7b - 6)(15a - 3) \]

### Problem 17:
\[ 16x^2c + 8xyd - 16x^2d - 8xyc \]

**Step 1**: Group like terms for factoring.

- Rearrange the expression:
\[ = (16x^2c - 16x^2d) + (8xyd - 8xyc) \]

- Factor out common terms:
\[ = 16x^2(c - d) + 8xy(d - c) \]

- Combine similar terms:
\[ = 16x^2(c - d) - 8xy(c - d) \]

- Factor out the common binomial:
\[ = (c - d)(16x^2 - 8xy) \]

### Problem 18:
\[ 150m^2nz + 20mn^2c - 120m^2nc - 25mn^2z \]

**Step 1**: Group like terms.

- Group terms:
\[ = (150m^2nz - 25mn^2z) + (20mn^2c - 120m^2nc) \]

- Factor out common terms:
\[ = 25mnz(6m - n) + 20mnc(n - 6m) \]

- Combine them:
\[ = 25mnz(6m - n) - 20mnc(6m - n) \]

- Factor out the common binomial:
\[ = (6m - n)(25mnz - 20mnc) \]

Would you like me to continue with the remaining problems or go into further detail on any specific step? Here are some related questions to consider:

1. What techniques are useful in factoring complex expressions?
2. How do you recognize when an expression can be factored?
3. What are some strategies for grouping terms efficiently?
4. How can you check if your factorization is correct?
5. What common mistakes should be avoided when simplifying expressions?

**Tip**: Always check for the greatest common factor (GCF) first when factoring—it simplifies the process significantly!

Algebraic expressions involving terms like 192x^2y + 72x^3 - 24rxy - 9x^2 and similar problems requiring simplification or factoring.

Learn how to factor and simplify algebraic expressions like 192x^2y + 72x^3 - 24rxy - 9x^2. This lesson covers essential algebra concepts such as grouping terms and factoring common elements, suitable for Grades 9-12 students.

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