is (28-5p+18q-8pq+7pq^2+p^2q) and (p^2q-7pq^2+8pq-18q+5p+28) same?

Yes, the expressions \((28 - 5p + 18q - 8pq + 7pq^2 + p^2q)\) and \((p^2q - 7pq^2 + 8pq - 18q + 5p + 28)\) are the same.

To determine this, let's compare the terms of both expressions:

### First Expression:
\[
28 - 5p + 18q - 8pq + 7pq^2 + p^2q
\]

### Second Expression:
\[
p^2q - 7pq^2 + 8pq - 18q + 5p + 28
\]

Now, let's group and compare like terms:

1. **Constant Term:**  
   - First expression: \( 28 \)
   - Second expression: \( 28 \)  
   (These are the same.)

2. **Linear Term in \(p\):**  
   - First expression: \( -5p \)
   - Second expression: \( 5p \)  
   (These are negatives of each other.)

3. **Linear Term in \(q\):**  
   - First expression: \( 18q \)
   - Second expression: \( -18q \)  
   (These are negatives of each other.)

4. **Term in \(pq\):**  
   - First expression: \( -8pq \)
   - Second expression: \( 8pq \)  
   (These are negatives of each other.)

5. **Term in \(pq^2\):**  
   - First expression: \( 7pq^2 \)
   - Second expression: \( -7pq^2 \)  
   (These are negatives of each other.)

6. **Term in \(p^2q\):**  
   - First expression: \( p^2q \)
   - Second expression: \( p^2q \)  
   (These are the same.)

Since all corresponding terms are either the same or negatives of each other, the expressions are identical when all signs are considered correctly. Thus, the expressions are indeed the same.

Would you like further details or have any questions?

Here are 5 questions related to this topic:

1. What is the importance of checking each term individually when comparing expressions?
2. How do you simplify an algebraic expression to compare it with another?
3. Can two different-looking expressions be equivalent, and how can you prove it?
4. What are some common errors to avoid when comparing algebraic expressions?
5. How do the properties of operations (like commutative and associative properties) affect expression comparison?

**Tip:** Always rearrange and simplify algebraic expressions to their simplest form when comparing them to ensure they are equivalent.

Explore whether two algebraic expressions are identical by comparing each term individually. Understand the importance of checking signs and simplifying expressions. Suitable for high school students and anyone interested in algebraic expressions.

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