Simplify the algebraic expression:(3x-y)(4x-5y).

To simplify the expression \((3x-y)(4x-5y)\), we will apply the distributive property (also known as the FOIL method when dealing with two binomials):

### Step-by-Step Solution

1. **Expand the expression using FOIL**:
   
   \[
   (3x - y)(4x - 5y) = (3x) \cdot (4x) + (3x) \cdot (-5y) + (-y) \cdot (4x) + (-y) \cdot (-5y)
   \]
   
2. **Multiply each term**:
   
   - \( (3x) \cdot (4x) = 12x^2 \)
   - \( (3x) \cdot (-5y) = -15xy \)
   - \( (-y) \cdot (4x) = -4xy \)
   - \( (-y) \cdot (-5y) = 5y^2 \)

3. **Combine like terms** (the \( xy \) terms):
   
   \[
   12x^2 - 15xy - 4xy + 5y^2
   \]
   
   Simplify the \( xy \) terms:
   
   \[
   12x^2 - 19xy + 5y^2
   \]

### Final Answer
\[
12x^2 - 19xy + 5y^2
\]

Do you want details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would you factor the expression \( 12x^2 - 19xy + 5y^2 \)?
2. What is the result of simplifying \( (2x + 3y)(3x - 2y) \)?
3. How do you apply the FOIL method to three or more terms in parentheses?
4. Can you identify when terms are like terms for combining?
5. What if \( x \) or \( y \) had a negative coefficient initially, how would that change the process?

**Tip**: Remember, when multiplying

Simplify the algebraic expression: (3x - y)(4x - 5y).

Learn how to simplify the algebraic expression (3x - y)(4x - 5y) using the distributive property (FOIL method). This step-by-step guide covers essential algebraic concepts like combining like terms and applying the distributive property. Perfect for students in Grades 8-10.

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