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The given expression is:

\[
(3x^2 - 10x - 2) - (6x + 3)
\]

Let's simplify this step by step.

1. Distribute the negative sign to each term inside the second set of parentheses:
\[
3x^2 - 10x - 2 - 6x - 3
\]

2. Combine like terms:
- The \(x^2\) terms: \(3x^2\) (no other \(x^2\) terms to combine)
- The \(x\) terms: \(-10x - 6x = -16x\)
- The constant terms: \(-2 - 3 = -5\)

Thus, the simplified expression is:

\[
3x^2 - 16x - 5
\]

So the final answer is:
\[
\boxed{3x^2 - 16x - 5}
\]

Would you like more details on any step or have any questions? Here are five related questions to explore:

1. How do you simplify an expression with parentheses and a negative sign?
2. What are like terms in algebraic expressions?
3. Can you explain how to factor the simplified expression \(3x^2 - 16x - 5\)?
4. How would the process change if one of the terms had a fractional coefficient?
5. What if the expression had a cubic term? How would that affect the simplification?

**Tip:** Always distribute negative signs carefully when subtracting expressions inside parentheses!

Learn how to simplify the algebraic expression (3x^2 - 10x - 2) - (6x + 3) by distributing the negative sign and combining like terms. This step-by-step solution explains key concepts in algebra suitable for students in Grades 7-9.

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