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### Extracted Mathematical Problems

1. **Multiply each of the following:**
   \[
   \text{(a)} \, (3p + 2q) \cdot (p + 4r) 
   \]
   \[
   \text{(b)} \, (3m - 5n) \cdot (3m + 5n)
   \]

2. **Find the product of the following:**
   \[
   \text{(a)} \, (2x - 3y)(7x^2 - 2xy + 5y^2) 
   \]
   \[
   \text{(b)} \, (4x + 5y - z)(2x - 3y + 2z)
   \]

3. **Simplify the following:**
   \[
   \text{(a)} \, 6a(2b + c) - 4a(a - b) 
   \]
   \[
   \text{(b)} \, (7x - 3y)(x + y) + 2xy
   \]

4. **Find the sum of:**
   \[
   \text{(a)} \, 3x(2x - 3y) - 2y(4x + 5y)
   \]
   \[
   \text{(b)} \, 4x(5x + 2y) - 3y(3x - y)
   \]

5. **Subtract and simplify the result:**
   \[
   \text{(a)} \, 6x^2 + 7x - 3 \text{ from } 3x^2 + 2x + 4
   \]
   \[
   \text{(b)} \, 9x^2 - 4x + 7 \text{ from } 5x^2 + 3x - 2
   \]

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Multiply, find products, simplify, and subtract various algebraic expressions as provided in the given list of problems.

Solve various algebraic problems involving multiplication, simplification, and subtraction of polynomials. This page covers essential algebraic concepts like the distributive property and simplification of like terms, suitable for students in Grades 8-10.

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