(x + a) (x + b) = `x^(2)` + (a + b)x + ________.

Options

A. `ab^2`
B. `a^2b`
C. ab
D. `a^2b^2`

Answer

To solve the equation \((x + a)(x + b) = x^2 + (a + b)x + \_\_\_\_\_\_\_\_\), we will expand the left-hand side and identify the missing term.

### Step-by-Step Solution:

1. **Write down the expression to be expanded**:
\[ (x + a)(x + b) \]

2. **Use the distributive property (FOIL method)**:
- First, multiply the first terms: \(x \cdot x = x^2\)
- Outer: \(x \cdot b = bx\)
- Inner: \(a \cdot x = ax\)
- Last: \(a \cdot b = ab\)

Putting these together, we have:
\[ x^2 + bx + ax + ab \]

3. **Combine like terms**:
- The terms \(bx\) and \(ax\) can be combined:
\[ x^2 + (a + b)x + ab \]

4. **Identify the missing term**:
- From the expression \(x^2 + (a + b)x + ab\), we see that the blank in the original equation corresponds to \(ab\).

Thus, the complete equation is:
\[ (x + a)(x + b) = x^2 + (a + b)x + ab \]

### Final Answer:
The missing term is \(ab\).

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