To solve the problem of subtracting the polynomial [tex]\( 9a^2 - 6a + 5 \)[/tex] from [tex]\( 10a^2 + 3a + 25 \)[/tex], follow these steps:
### Step-by-Step Solution:
1. Write down the polynomials:
[tex]\[
10a^2 + 3a + 25
\][/tex]
[tex]\[
9a^2 - 6a + 5
\][/tex]
2. Set up the subtraction:
[tex]\[
(10a^2 + 3a + 25) - (9a^2 - 6a + 5)
\][/tex]
Distribute the negative sign to the second polynomial:
[tex]\[
10a^2 + 3a + 25 - 9a^2 + 6a - 5
\][/tex]
3. Combine like terms:
- Combine the [tex]\( a^2 \)[/tex] terms:
[tex]\[
10a^2 - 9a^2 = a^2
\][/tex]
- Combine the [tex]\( a \)[/tex] terms:
[tex]\[
3a + 6a = 9a
\][/tex]
- Combine the constant terms:
[tex]\[
25 - 5 = 20
\][/tex]
4. Write the resulting polynomial in standard form:
[tex]\[
a^2 + 9a + 20
\][/tex]
Therefore, the polynomial obtained after subtracting [tex]\( 9a^2 - 6a + 5 \)[/tex] from [tex]\( 10a^2 + 3a + 25 \)[/tex] is:
[tex]\[
\boxed{a^2 + 9a + 20}
\][/tex]
