List of four algebraic expressions with coefficients and quadratic terms.

Let’s solve each problem step by step. These are all distributive property problems — we multiply the number or term outside the parentheses by every term inside.

---

Problem 1: 3(x² + 2x + 6)

Multiply 3 by each term inside:

- 3 × x² = 3x²
- 3 × 2x = 6x
- 3 × 6 = 18

So, result is:
→ 3x² + 6x + 18

---

Problem 3: 2(x² - x + 11)

Multiply 2 by each term:

- 2 × x² = 2x²
- 2 × (-x) = -2x
- 2 × 11 = 22

Result:
→ 2x² - 2x + 22

---

Problem 5: -3x(x² - 7x + 1)

Multiply -3x by each term:

- -3x × x² = -3x³
- -3x × (-7x) = +21x² (because negative times negative is positive)
- -3x × 1 = -3x

Result:
→ -3x³ + 21x² - 3x

---

Problem 7: 5x(-2x² + 8x + 12)

Multiply 5x by each term:

- 5x × (-2x²) = -10x³
- 5x × 8x = 40x²
- 5x × 12 = 60x

Result:
→ -10x³ + 40x² + 60x

---

Final Answer:
1. 3x² + 6x + 18
3. 2x² - 2x + 22
5. -3x³ + 21x² - 3x
7. -10x³ + 40x² + 60x