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To expand and simplify the expression \((2x + 1)(x + 6)\), let's proceed by using the distributive property, also known as the FOIL method for binomials:

### Step-by-Step Solution
1. **First terms:** \(2x \cdot x = 2x^2\)
2. **Outside terms:** \(2x \cdot 6 = 12x\)
3. **Inside terms:** \(1 \cdot x = x\)
4. **Last terms:** \(1 \cdot 6 = 6\)

### Combine All Terms
Now we add all these terms together:
\[
2x^2 + 12x + x + 6
\]

### Simplify by Combining Like Terms
\[
2x^2 + 13x + 6
\]

### Final Answer
\[
2x^2 + 13x + 6
\]

Let me know if you need further clarification or more details.

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Here are five related questions for further practice:
1. Expand and simplify \((3x + 2)(x + 5)\).
2. Expand and simplify \((x + 4)(x + 7)\).
3. Expand and simplify \((2x + 3)(2x + 5)\).
4. How would you expand \((x - 2)(x + 3)\)?
5. Can you factor the result \(2x^2 + 13x + 6\)?

**Tip:** Remember to combine like terms carefully when expanding expressions to ensure accuracy.

Learn how to expand and simplify the expression (2x + 1)(x + 6) using the distributive property. This problem involves algebraic concepts and polynomial expansion, suitable for students in Grades 8-10.

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