## Simplifying the Expression: (d² + 6d + 9) - (d³ + 6d + 9)

This problem involves simplifying an algebraic expression by subtracting two polynomials. Here's a step-by-step guide:

### 1. Distribute the Negative Sign

First, we distribute the negative sign in front of the second set of parentheses:

(d² + 6d + 9) **-** (d³ + 6d + 9) = d² + 6d + 9 **-** d³ **-** 6d **-** 9

### 2. Combine Like Terms

Next, we identify and combine like terms:

**d²:**We have one term with d²:**d²****d³:**We have one term with d³:**-d³****d:**We have two terms with d:**6d - 6d = 0****Constant:**We have two constant terms:**9 - 9 = 0**

### 3. Simplified Expression

After combining like terms, the simplified expression becomes:

**-d³ + d²**

### Conclusion

Therefore, the simplified form of the expression (d² + 6d + 9) - (d³ + 6d + 9) is **-d³ + d²**.