To simplify the expression \( 2(6a - 5b + 1) \), we can distribute the \( 2 \) to each term inside the parentheses.

\[
2(6a - 5b + 1) = 2 \times 6a - 2 \times 5b + 2 \times 1
\]

This simplifies to:

\[
12a - 10b + 2
\]

So, the simplified expression is:

\[
12a - 10b + 2
\]

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:
1. How would you factor \(12a - 10b + 2\)?
2. What happens if we distribute a negative number instead?
3. How can you simplify \(3(4a - 2b + 5)\)?
4. Can you solve an equation if \(2(6a - 5b + 1) = 0\)?
5. What is the result of distributing in \( -2(6a + 5b - 3)\)?

**Tip:** When distributing a constant, make sure to apply it to every term inside the parentheses!

Learn how to simplify the algebraic expression 2(6a - 5b + 1) step-by-step by applying the distributive property. This problem introduces key algebraic concepts, including how to distribute constants across terms. Ideal for students in Grades 6-8.

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