Let's simplify the expression \( 3x(2x + 3) - x(3x + 5) \) step by step:

1. **Distribute** the terms:
   \[
   3x(2x + 3) = 3x \cdot 2x + 3x \cdot 3 = 6x^2 + 9x
   \]
   \[
   -x(3x + 5) = -x \cdot 3x - x \cdot 5 = -3x^2 - 5x
   \]

2. **Combine like terms**:
   \[
   (6x^2 + 9x) - (3x^2 + 5x) = 6x^2 + 9x - 3x^2 - 5x
   \]
   \[
   = (6x^2 - 3x^2) + (9x - 5x) = 3x^2 + 4x
   \]

So, the simplified expression is:
\[
3x^2 + 4x
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factor the expression \( 3x^2 + 4x \)?
2. What are the roots of the quadratic equation \( 3x^2 + 4x = 0 \)?
3. How does distributing affect terms in an algebraic expression?
4. Can you apply the same method to simplify \( 4x(3x - 2) - 2x(5x + 1) \)?
5. How does combining like terms simplify polynomial expressions?

**Tip:** Always handle negative signs carefully when distributing terms.

Learn how to simplify the polynomial expression 3x(2x+3)-x(3x+5) using distribution and combining like terms. This step-by-step solution is ideal for students in Grades 8-10, covering key algebraic concepts such as distribution and polynomial simplification.

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