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.

Learn how to subtract polynomials step-by-step: 10a^2 + 3a + 25 - (9a^2 - 6a + 5). This problem involves combining like terms and understanding polynomial subtraction. Suitable for students in Grades 7-9.

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