Solve `(x+9) (x^(2) +5)`.

Options

A. `x^(2) + x+ 14`
B. `x^(3) + 9x^(2) + 5x +45`
C. `x^(3) + 45`
D. None of these

Answer

To solve the expression \((x + 9)(x^2 + 5)\), we will use the distributive property (also known as the FOIL method for binomials). Here are the steps:

### Step-by-Step Solution

1. **Distribute \(x\) to both terms in the second expression**:
\[ x \cdot (x^2 + 5) = x \cdot x^2 + x \cdot 5 = x^3 + 5x \]

2. **Distribute \(9\) to both terms in the second expression**:
\[ 9 \cdot (x^2 + 5) = 9 \cdot x^2 + 9 \cdot 5 = 9x^2 + 45 \]

3. **Combine all the terms obtained from the distributions**:
\[ x^3 + 5x + 9x^2 + 45 \]

4. **Rearrange the terms in standard form** (from highest degree to lowest):
\[ x^3 + 9x^2 + 5x + 45 \]

Thus, the final expression after solving \((x + 9)(x^2 + 5)\) is:
\[ \boxed{x^3 + 9x^2 + 5x + 45} \]