Let's simplify the expression step by step:

Given:
$3(a + 2) - 6a - 3$

1. Distribute the 3 across the terms inside the parentheses: $3 \times a + 3 \times 2 = 3a + 6$

   So the expression becomes: $3a + 6 - 6a - 3$

2. Combine like terms:

   • Combine the terms with $a$: $3a - 6a = -3a$
   • Combine the constant terms: $6 - 3 = 3$

   Therefore, the simplified expression is: $-3a + 3$

So, the simplified form of the expression is: $-3a + 3$

Would you like more details on any step or have questions?

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Here are 5 related questions to explore:

1. How do you simplify expressions with multiple variables?
2. What happens when you distribute negative numbers in expressions?
3. How would you solve for $a$ if this were set equal to zero?
4. How do you factor expressions like $-3a + 3$?
5. How do you expand binomials like $(a + 2)(b + 3)$?

Tip: Always distribute carefully, especially when negative signs are involved to avoid sign errors.