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.