This printable algebra worksheet helps students practice evaluating expressions and simplifying terms.

Problem: Solve the algebraic expressions and combine like terms as per the instructions in the image.

#### Part I: Complete the expressions using the order of operations.

The order of operations is often remembered by the acronym PEMDAS:
1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Let's solve each expression step by step.

---

#### Expression 1:
$$
6 + 18 \div 9 - 2 \times 2
$$
1. Perform division and multiplication first:
$$
18 \div 9 = 2 \quad \text{and} \quad 2 \times 2 = 4
$$
2. Substitute these values back into the expression:
$$
6 + 2 - 4
$$
3. Perform addition and subtraction from left to right:
$$
6 + 2 = 8 \quad \text{and} \quad 8 - 4 = 4
$$
Answer: $\boxed{4}$

---

#### Expression 2:
$$
10 \div 5 - 7 \times 1 - 5
$$
1. Perform division and multiplication first:
$$
10 \div 5 = 2 \quad \text{and} \quad 7 \times 1 = 7
$$
2. Substitute these values back into the expression:
$$
2 - 7 - 5
$$
3. Perform subtraction from left to right:
$$
2 - 7 = -5 \quad \text{and} \quad -5 - 5 = -10
$$
Answer: $\boxed{-10}$

---

#### Expression 3:
$$
8 \times 3 - 4 + 12 \div 2
$$
1. Perform multiplication and division first:
$$
8 \times 3 = 24 \quad \text{and} \quad 12 \div 2 = 6
$$
2. Substitute these values back into the expression:
$$
24 - 4 + 6
$$
3. Perform addition and subtraction from left to right:
$$
24 - 4 = 20 \quad \text{and} \quad 20 + 6 = 26
$$
Answer: $\boxed{26}$

---

#### Expression 4:
$$
20 - 3 \times 3 + 10 \div 2
$$
1. Perform multiplication and division first:
$$
3 \times 3 = 9 \quad \text{and} \quad 10 \div 2 = 5
$$
2. Substitute these values back into the expression:
$$
20 - 9 + 5
$$
3. Perform addition and subtraction from left to right:
$$
20 - 9 = 11 \quad \text{and} \quad 11 + 5 = 16
$$
Answer: $\boxed{16}$

---

#### Expression 5:
$$
21 + 3 \cdot 7 - 4 \times 1
$$
1. Perform multiplication first:
$$
3 \cdot 7 = 21 \quad \text{and} \quad 4 \times 1 = 4
$$
2. Substitute these values back into the expression:
$$
21 + 21 - 4
$$
3. Perform addition and subtraction from left to right:
$$
21 + 21 = 42 \quad \text{and} \quad 42 - 4 = 38
$$
Answer: $\boxed{38}$

---

#### Expression 6:
$$
4 \times 6 - 20 + 24 \div 3
$$
1. Perform multiplication and division first:
$$
4 \times 6 = 24 \quad \text{and} \quad 24 \div 3 = 8
$$
2. Substitute these values back into the expression:
$$
24 - 20 + 8
$$
3. Perform addition and subtraction from left to right:
$$
24 - 20 = 4 \quad \text{and} \quad 4 + 8 = 12
$$
Answer: $\boxed{12}$

---

#### Expression 7:
$$
11 - 2 \times 5 + 14 \div 7
$$
1. Perform multiplication and division first:
$$
2 \times 5 = 10 \quad \text{and} \quad 14 \div 7 = 2
$$
2. Substitute these values back into the expression:
$$
11 - 10 + 2
$$
3. Perform addition and subtraction from left to right:
$$
11 - 10 = 1 \quad \text{and} \quad 1 + 2 = 3
$$
Answer: $\boxed{3}$

---

#### Expression 8:
$$
9 + 6 \times 5 - 16 \div 1
$$
1. Perform multiplication and division first:
$$
6 \times 5 = 30 \quad \text{and} \quad 16 \div 1 = 16
$$
2. Substitute these values back into the expression:
$$
9 + 30 - 16
$$
3. Perform addition and subtraction from left to right:
$$
9 + 30 = 39 \quad \text{and} \quad 39 - 16 = 23
$$
Answer: $\boxed{23}$

---

Part II: Combine like terms.

Combine like terms means grouping together terms that have the same variable(s) and exponent(s).

---

#### Expression 9:
$$
3x + 4x
$$
1. Both terms have the same variable $x$, so add their coefficients:
$$
3x + 4x = 7x
$$
Answer: $\boxed{7x}$

---

#### Expression 10:
$$
10x - 3x
$$
1. Both terms have the same variable $x$, so subtract their coefficients:
$$
10x - 3x = 7x
$$
Answer: $\boxed{7x}$

---

#### Expression 11:
$$
x + 7x
$$
1. Both terms have the same variable $x$, so add their coefficients:
$$
x + 7x = 8x
$$
Answer: $\boxed{8x}$

---

#### Expression 12:
$$
2y + 9y
$$
1. Both terms have the same variable $y$, so add their coefficients:
$$
2y + 9y = 11y
$$
Answer: $\boxed{11y}$

---

#### Expression 13:
$$
5y - 4y
$$
1. Both terms have the same variable $y$, so subtract their coefficients:
$$
5y - 4y = y
$$
Answer: $\boxed{y}$

---

#### Expression 14:
$$
12y - 3y
$$
1. Both terms have the same variable $y$, so subtract their coefficients:
$$
12y - 3y = 9y
$$
Answer: $\boxed{9y}$

---

#### Expression 15:
$$
2x + 5y - x
$$
1. Group like terms:
- Terms with $x$: $2x - x = x$
- Term with $y$: $5y$ (no other $y$-terms)
$$
x + 5y
$$
Answer: $\boxed{x + 5y}$

---

#### Expression 16:
$$
4y - 4x + 2y
$$
1. Group like terms:
- Terms with $y$: $4y + 2y = 6y$
- Term with $x$: $-4x$ (no other $x$-terms)
$$
-4x + 6y
$$
Answer: $\boxed{-4x + 6y}$

---

#### Expression 17:
$$
5x + 2y - x + 4y
$$
1. Group like terms:
- Terms with $x$: $5x - x = 4x$
- Terms with $y$: $2y + 4y = 6y$
$$
4x + 6y
$$
Answer: $\boxed{4x + 6y}$

---

#### Expression 18:
$$
10y - 2y - 3x + 9x
$$
1. Group like terms:
- Terms with $y$: $10y - 2y = 8y$
- Terms with $x$: $-3x + 9x = 6x$
$$
6x + 8y
$$
Answer: $\boxed{6x + 8y}$

---

#### Expression 19:
$$
x + y + 6x + 7y
$$
1. Group like terms:
- Terms with $x$: $x + 6x = 7x$
- Terms with $y$: $y + 7y = 8y$
$$
7x + 8y
$$
Answer: $\boxed{7x + 8y}$

---

#### Expression 20:
$$
2y + 8y - 3x + y
$$
1. Group like terms:
- Terms with $y$: $2y + 8y + y = 11y$
- Term with $x$: $-3x$ (no other $x$-terms)
$$
-3x + 11y
$$
Answer: $\boxed{-3x + 11y}$

---

Final Answers:

1. $\boxed{4}$
2. $\boxed{-10}$
3. $\boxed{26}$
4. $\boxed{16}$
5. $\boxed{38}$
6. $\boxed{12}$
7. $\boxed{3}$
8. $\boxed{23}$
9. $\boxed{7x}$
10. $\boxed{7x}$
11. $\boxed{8x}$
12. $\boxed{11y}$
13. $\boxed{y}$
14. $\boxed{9y}$
15. $\boxed{x + 5y}$
16. $\boxed{-4x + 6y}$
17. $\boxed{4x + 6y}$
18. $\boxed{6x + 8y}$
19. $\boxed{7x + 8y}$
20. $\boxed{-3x + 11y}$

$\boxed{\text{All answers are provided above.}}$