You want to subtract the expression $9a^2 - 6a + 5$ from $10a^2 + 3a + 25$. Here's how to do it step by step:

1. Write down the expressions:

   $(10a^2 + 3a + 25) - (9a^2 - 6a + 5)$

2. Distribute the negative sign across the second expression:

   $10a^2 + 3a + 25 - 9a^2 + 6a - 5$

3. Combine like terms:

   $(10a^2 - 9a^2) + (3a + 6a) + (25 - 5)$

   Simplifying further:

   $a^2 + 9a + 20$

So, the result of subtracting $9a^2 - 6a + 5$ from $10a^2 + 3a + 25$ is:

$a^2 + 9a + 20$

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you factorize the expression $a^2 + 9a + 20$?
2. What would happen if you added the expressions instead of subtracting them?
3. How would you solve $a^2 + 9a + 20 = 0$ using the quadratic formula?
4. Can you perform the same operation if the coefficients of $a^2$ or $a$ were fractions?
5. What real-world applications can you think of for quadratic expressions like this?

Tip: When subtracting polynomials, always distribute the negative sign carefully to each term in the second polynomial.