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It appears you've uploaded an image with several algebraic expressions. I will solve and simplify each one of them for you. Let’s go through each:

1. **\( a(b - c + d) \)**
   \[
   \text{Simplification: } ab - ac + ad
   \]
   This is a basic distribution of \(a\) over the terms inside the parentheses.

2. **\( (p + q - r)x \)**
   \[
   \text{Simplification: } px + qx - rx
   \]
   Distribute \(x\) to each term inside the parentheses.

3. **\( (-3x)(x^2 - 5x + 6) \)**
   \[
   \text{Simplification: } -3x^3 + 15x^2 - 18x
   \]
   Multiply \(-3x\) with each term inside the parentheses.

4. **\( x^2(y^2 + z^2 - x^2) \)**
   \[
   \text{Simplification: } x^2y^2 + x^2z^2 - x^4
   \]
   Multiply \(x^2\) with each term inside the parentheses.

5. **\( (2ab)(a^2 - ab + b^2) \)**
   \[
   \text{Simplification: } 2a^3b - 2a^2b^2 + 2ab^3
   \]
   Distribute \(2ab\) over the terms inside the parentheses.

6. **\( x^3(x^2 - x + 2) \)**
   \[
   \text{Simplification: } x^5 - x^4 + 2x^3
   \]
   Multiply \(x^3\) by each term in the parentheses.

7. **\( (-2xy^2)(x^2 - 3xy + 2y^2) \)**
   \[
   \text{Simplification: } -2x^3y^2 + 6x^2y^3 - 4xy^4
   \]
   Multiply \(-2xy^2\) by each term in the parentheses.

8. **\( (y^2 - yz + z^2)(y^2z^2) \)**
   \[
   \text{Simplification: } y^4z^2 - y^3z^3 + y^2z^4
   \]
   Multiply \(y^2z^2\) by each term in the parentheses.

Would you like more details on any of these steps, or have any specific questions?

Here are 5 related questions to extend this topic:
1. How can you identify when a term can be factored further?
2. What is the distributive property and why is it useful in simplifying expressions?
3. How would you handle similar expressions with fractional exponents?
4. How does simplification of polynomial expressions help in solving equations?
5. What are some real-world applications of polynomial simplifications?

**Tip:** Always watch for common factors when simplifying expressions, as this can speed up the process!

Simplify the following algebraic expressions: 1) a(b - c + d), 2) (p + q - r)x, 3) (-3x)(x^2 - 5x + 6), 4) x^2(y^2 + z^2 - x^2), 5) (2ab)(a^2 - ab + b^2), 6) x^3(x^2 - x + 2), 7) (-2xy^2)(x^2 - 3xy + 2y^2), 8) (y^2 - yz + z^2)(y^2z^2).

Simplify algebraic expressions like a(b - c + d) and (2ab)(a^2 - ab + b^2) using the distributive property and polynomial multiplication. This guide covers key algebraic concepts and is suitable for students in Grades 8-10.

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