To simplify the expression:

\[
a + 4a^2 + 6a + 5a^2 + 7a + 10a^2 + 5a + 4
\]

Let's combine like terms:

1. Combine all the \(a^2\) terms:
   \[
   4a^2 + 5a^2 + 10a^2 = 19a^2
   \]

2. Combine all the \(a\) terms:
   \[
   a + 6a + 7a + 5a = 19a
   \]

3. Finally, combine the constant term:
   \[
   4
   \]

Now, the simplified expression is:
\[
19a^2 + 19a + 4
\]

Let me know if you'd like further details or have any questions! Here are 5 related questions for further practice:

1. Simplify: \(2a^2 + 3a + 4a^2 + 5a + 6\)
2. Factor the expression: \(19a^2 + 19a + 4\)
3. Simplify: \(3b + 2b^2 + 7b + 5b^2 + 8\)
4. Expand: \((a + 3)(2a + 5)\)
5. Solve: \(2x^2 + 3x + 4 = 0\)

**Tip:** When simplifying expressions, always group similar terms (like powers) to reduce complexity.

a + 4a² + 6a + 5a² + 7a + 10a² + 5a + 4

Learn how to simplify the algebraic expression a + 4a² + 6a + 5a² + 7a + 10a² + 5a + 4 by combining like terms. This problem involves key algebra concepts such as simplifying quadratic and linear terms. Ideal for students in Grades 6-8.

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