Solve these expressions 3(3x-4y), 3x+2(6x-6y), 4y-3(3x-7y), 3(3x+2y)-8y, -3(3x-7y)+2y

Let's solve each of these expressions one by one:

1. **Expression 1: \( 3(3x - 4y) \)**

   Apply the distributive property:

   \[
   3(3x - 4y) = 3 \cdot 3x - 3 \cdot 4y = 9x - 12y
   \]

   **Solution:** \( 9x - 12y \)

2. **Expression 2: \( 3x + 2(6x - 6y) \)**

   Apply the distributive property:

   \[
   3x + 2(6x - 6y) = 3x + 2 \cdot 6x - 2 \cdot 6y = 3x + 12x - 12y
   \]
   
   Combine like terms:

   \[
   3x + 12x = 15x
   \]

   **Solution:** \( 15x - 12y \)

3. **Expression 3: \( 4y - 3(3x - 7y) \)**

   Apply the distributive property:

   \[
   4y - 3(3x - 7y) = 4y - 3 \cdot 3x + 3 \cdot 7y = 4y - 9x + 21y
   \]
   
   Combine like terms:

   \[
   4y + 21y = 25y
   \]

   **Solution:** \( -9x + 25y \)

4. **Expression 4: \( 3(3x + 2y) - 8y \)**

   Apply the distributive property:

   \[
   3(3x + 2y) - 8y = 3 \cdot 3x + 3 \cdot 2y - 8y = 9x + 6y - 8y
   \]
   
   Combine like terms:

   \[
   6y - 8y = -2y
   \]

   **Solution:** \( 9x - 2y \)

5. **Expression 5: \( -3(3x - 7y) + 2y \)**

   Apply the distributive property:

   \[
   -3(3x - 7y) + 2y = -3 \cdot 3x + (-3) \cdot (-7y) + 2y = -9x + 21y + 2y
   \]
   
   Combine like terms:

   \[
   21y + 2y = 23y
   \]

   **Solution:** \( -9x + 23y \)

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**Summary of Solutions:**
1. \( 9x - 12y \)
2. \( 15x - 12y \)
3. \( -9x + 25y \)
4. \( 9x - 2y \)
5. \( -9x + 23y \)

Would you like any further details or explanations? Here are some related questions:

1. What is the distributive property and how does it work in simplifying expressions?
2. How do you combine like terms in an expression?
3. How would you simplify expressions with more variables or constants?
4. Can you explain how to factor expressions once they are simplified?
5. How would you approach solving equations involving these expressions?

**Tip:** Always distribute the constants first, then combine like terms to simplify expressions effectively!

This page covers the step-by-step process of solving algebraic expressions using the distributive property. Learn how to simplify expressions like 3(3x - 4y), 3x + 2(6x - 6y), and more by applying distributive property and combining like terms. Ideal for Grades 7-9.

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