Let's work through the problem step-by-step to subtract the given polynomials.
Given polynomials:
1. [tex]\(14a^2 - 24a + 7\)[/tex]
2. [tex]\(11a^2 + 42a - 6\)[/tex]
We need to subtract the second polynomial from the first polynomial. This means we need to perform the following operations on the corresponding coefficients:
### Step-by-Step Solution:
1. Subtract the coefficients of [tex]\(a^2\)[/tex]:
[tex]\[
14a^2 - 11a^2 = 3a^2
\][/tex]
2. Subtract the coefficients of [tex]\(a\)[/tex]:
[tex]\[
-24a - 42a = -66a
\][/tex]
3. Subtract the constant terms:
[tex]\[
7 - (-6) = 7 + 6 = 13
\][/tex]
### Combine the results:
[tex]\[
3a^2 - 66a + 13
\][/tex]
So, the polynomial resulting from the subtraction [tex]\( (14a^2 - 24a + 7) - (11a^2 + 42a - 6) \)[/tex] is [tex]\( \boxed{3a^2 - 66a + 13} \)[/tex].
Place this answer in descending powers of [tex]\(a\)[/tex], which is already in the correct format:
[tex]\[
3a^2 - 66a + 13
\][/tex]
