To simplify the expression $2(2b - 3c) + 3(4b + 3c)$, we need to distribute the constants $2$ and $3$ through each term in the parentheses. Here's how it goes:

1. Distribute $2$ in the first term: $2 \cdot 2b - 2 \cdot 3c = 4b - 6c$

2. Distribute $3$ in the second term: $3 \cdot 4b + 3 \cdot 3c = 12b + 9c$

3. Substitute these results back into the expression: $4b - 6c + 12b + 9c$

4. Combine like terms:

   • Combine the terms with $b$: $4b + 12b = 16b$
   • Combine the terms with $c$: $-6c + 9c = 3c$

5. The simplified expression is: $16b + 3c$

Would you like more details or have any questions?

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1. How can we further simplify similar expressions?
2. Why is distribution important in expressions?
3. How do we identify like terms in more complex expressions?
4. What changes if we have variables instead of constants for distribution?
5. How does this process apply to polynomials?

Tip: When distributing, always check that each term inside the parentheses is multiplied by the factor outside.