Let's simplify the given expression step by step:

\[
2a^2 - 7a + 5 + 6a^2 - 1
\]

1. Combine the like terms:
   - \(2a^2\) and \(6a^2\)
   - \(-7a\) (no other like terms)
   - \(5\) and \(-1\)

\[
(2a^2 + 6a^2) - 7a + (5 - 1)
\]

2. Simplify:
   - \(2a^2 + 6a^2 = 8a^2\)
   - \(5 - 1 = 4\)

So, the simplified expression is:

\[
8a^2 - 7a + 4
\]

Would you like more details or have any other questions?

Here are 5 related questions to deepen your understanding:
1. How do you combine like terms in a polynomial?
2. What is the degree of the polynomial \(8a^2 - 7a + 4\)?
3. How do you factor the expression \(8a^2 - 7a + 4\)?
4. Can this expression be simplified further or solved for specific values of \(a\)?
5. How do you graph the quadratic function \(8a^2 - 7a + 4\)?

**Tip**: Always group and combine like terms first when simplifying expressions, as it helps in reducing complexity.

Learn how to simplify the polynomial expression 2a² - 7a + 5 + 6a² - 1 with a detailed step-by-step explanation. This problem introduces key algebraic concepts such as combining like terms, suitable for students in Grades 6-8.

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