Sure! Let's solve this step by step.
We are given the expression:
[tex]\[
\left(d^2 + 6d + 9\right) - \left(d^3 + 6d + 9\right)
\][/tex]
First, let's distribute the negative sign across the second polynomial:
[tex]\[
d^2 + 6d + 9 - d^3 - 6d - 9
\][/tex]
Now, we combine like terms by grouping the corresponding powers of [tex]\(d\)[/tex]:
1. For [tex]\(d^3\)[/tex]:
[tex]\[
-d^3
\][/tex]
2. For [tex]\(d^2\)[/tex]:
[tex]\[
+d^2
\][/tex]
3. For [tex]\(d^1\)[/tex]:
[tex]\[
6d - 6d = 0
\][/tex]
4. For the constant term:
[tex]\[
9 - 9 = 0
\][/tex]
So, putting it all together:
[tex]\[
-d^3 + d^2
\][/tex]
This is the polynomial result in the standard form.
Thus,
[tex]\[
\left(d^2 + 6d + 9\right) - \left(d^3 + 6d + 9\right) = d^2(1 - d)
\][/tex]
