To expand and simplify the expression \((3x - 5)(2x - 3)\), we will use the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last) for binomials.

1. **First**: Multiply the first terms of each binomial:  
   \[ 3x \cdot 2x = 6x^2 \]

2. **Outer**: Multiply the outer terms:  
   \[ 3x \cdot (-3) = -9x \]

3. **Inner**: Multiply the inner terms:  
   \[ (-5) \cdot 2x = -10x \]

4. **Last**: Multiply the last terms:  
   \[ (-5) \cdot (-3) = 15 \]

Now, add all these terms together:  
\[
6x^2 - 9x - 10x + 15
\]

Combine like terms:  
\[
6x^2 - 19x + 15
\]

Thus, the expanded and simplified expression is:
\[
6x^2 - 19x + 15
\]

Would you like further details or clarifications?

Here are some related questions for further practice:
1. Expand and simplify \((x + 4)(2x - 1)\).
2. Factor the expression \(6x^2 - 19x + 15\).
3. Expand and simplify \((4x - 2)(x + 5)\).
4. Solve for \(x\) if \( (3x - 5)(2x - 3) = 0 \).
5. Expand and simplify \((5x + 6)(x - 4)\).

**Tip:** When expanding binomials, remember to carefully distribute each term to avoid sign mistakes.

Learn how to expand and simplify the expression (3x-5)(2x-3) using the distributive property (FOIL method). This step-by-step guide simplifies the polynomial to 6x^2 - 19x + 15, helping students understand binomial expansion concepts. Suitable for Grades 8-10.

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