Is `7x^(2)-9x-3(-3x^(2)-3x+2)` a monomial or a binomial?

Answer

To determine whether the expression \( 7x^2 - 9x - 3(-3x^2 - 3x + 2) \) is a monomial or a binomial, we will first simplify the expression and then analyze the number of terms it contains.

### Step-by-Step Solution:

1. **Write down the expression**:
The expression we need to analyze is:
\[ 7x^2 - 9x - 3(-3x^2 - 3x + 2) \]

2. **Distribute the -3**:
We will distribute the -3 across the terms inside the parentheses:
\[ -3 \cdot (-3x^2) = 9x^2 \]
\[ -3 \cdot (-3x) = 9x \]
\[ -3 \cdot 2 = -6 \]
So, the expression becomes:
\[ 7x^2 - 9x + 9x^2 + 9x - 6 \]

3. **Combine like terms**:
Now we will combine the like terms:
- For \(x^2\) terms: \(7x^2 + 9x^2 = 16x^2\)
- For \(x\) terms: \(-9x + 9x = 0\)
- The constant term remains \(-6\).
Thus, the simplified expression is:
\[ 16x^2 - 6 \]

4. **Identify the number of terms**:
The simplified expression \(16x^2 - 6\) consists of two terms:
- The first term is \(16x^2\)
- The second term is \(-6\)

5. **Conclusion**:
Since the expression has two terms, it is classified as a **binomial**.

### Final Answer:
The expression \( 7x^2 - 9x - 3(-3x^2 - 3x + 2) \) is a **binomial**.