Let's find the polynomial that results from subtracting [tex]\(9a^2 - 6a + 5\)[/tex] from [tex]\(10a^2 + 3a + 25\)[/tex].
Follow these steps:
1. Write down the polynomials:
[tex]\[
(10a^2 + 3a + 25) - (9a^2 - 6a + 5)
\][/tex]
2. Distribute the negative sign to the second polynomial:
[tex]\[
10a^2 + 3a + 25 - 9a^2 + 6a - 5
\][/tex]
3. Combine like terms:
- For the [tex]\(a^2\)[/tex] terms:
[tex]\[
10a^2 - 9a^2 = 1a^2
\][/tex]
- For the [tex]\(a\)[/tex] terms:
[tex]\[
3a + 6a = 9a
\][/tex]
- For the constant terms:
[tex]\[
25 - 5 = 20
\][/tex]
4. Combine the results:
So, the result from the subtraction is:
[tex]\[
1a^2 + 9a + 20
\][/tex]
Therefore, when you subtract [tex]\(9a^2 - 6a + 5\)[/tex] from [tex]\(10a^2 + 3a + 25\)[/tex], the resulting polynomial is:
[tex]\[
1a^2 + 9a + 20
\][/tex]
