How to Simplify Algebraic Expressions | Worksheet - Free Printable

Problem: Simplify Algebraic Expressions

The task is to simplify a series of algebraic expressions using the distributive property and combining like terms. Let's solve each expression step by step.

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#### Expression 1: \( 4(x + 8) \)

1. Distribute the 4:
\[
4(x + 8) = 4 \cdot x + 4 \cdot 8
\]
2. Simplify:
\[
4x + 32
\]

Final Answer:
\[
\boxed{4x + 32}
\]

---

#### Expression 2: \( 10p - 5p + 4 \)

1. Combine like terms:
\[
10p - 5p = 5p
\]
2. Add the constant term:
\[
5p + 4
\]

Final Answer:
\[
\boxed{5p + 4}
\]

---

#### Expression 3: \( 9 + 2b + 8b \)

1. Combine like terms:
\[
2b + 8b = 10b
\]
2. Add the constant term:
\[
9 + 10b
\]

Final Answer:
\[
\boxed{9 + 10b}
\]

---

#### Expression 4: \( 7t - 6 - 5t \)

1. Combine like terms:
\[
7t - 5t = 2t
\]
2. Subtract the constants:
\[
2t - 6
\]

Final Answer:
\[
\boxed{2t - 6}
\]

---

#### Expression 5: \( 3(3a - 10) \)

1. Distribute the 3:
\[
3(3a - 10) = 3 \cdot 3a - 3 \cdot 10
\]
2. Simplify:
\[
9a - 30
\]

Final Answer:
\[
\boxed{9a - 30}
\]

---

#### Expression 6: \( 7(3m + 2) \)

1. Distribute the 7:
\[
7(3m + 2) = 7 \cdot 3m + 7 \cdot 2
\]
2. Simplify:
\[
21m + 14
\]

Final Answer:
\[
\boxed{21m + 14}
\]

---

#### Expression 7: \( 2h + 4(2h + 7) \)

1. Distribute the 4 inside the parentheses:
\[
4(2h + 7) = 4 \cdot 2h + 4 \cdot 7 = 8h + 28
\]
2. Combine with the original expression:
\[
2h + 8h + 28
\]
3. Combine like terms:
\[
2h + 8h = 10h
\]
4. Add the constant term:
\[
10h + 28
\]

Final Answer:
\[
\boxed{10h + 28}
\]

---

#### Expression 8: \( 10c + 8 - c - 3 \)

1. Combine like terms for \( c \):
\[
10c - c = 9c
\]
2. Combine the constants:
\[
8 - 3 = 5
\]
3. Combine results:
\[
9c + 5
\]

Final Answer:
\[
\boxed{9c + 5}
\]

---

#### Expression 9: \( 15 + 12y - 4 + 6y \)

1. Combine like terms for \( y \):
\[
12y + 6y = 18y
\]
2. Combine the constants:
\[
15 - 4 = 11
\]
3. Combine results:
\[
18y + 11
\]

Final Answer:
\[
\boxed{18y + 11}
\]

---

#### Expression 10: \( 9d + 6(d - 2) \)

1. Distribute the 6 inside the parentheses:
\[
6(d - 2) = 6 \cdot d - 6 \cdot 2 = 6d - 12
\]
2. Combine with the original expression:
\[
9d + 6d - 12
\]
3. Combine like terms:
\[
9d + 6d = 15d
\]
4. Add the constant term:
\[
15d - 12
\]

Final Answer:
\[
\boxed{15d - 12}
\]

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Final Answers:

1. \( \boxed{4x + 32} \)
2. \( \boxed{5p + 4} \)
3. \( \boxed{9 + 10b} \)
4. \( \boxed{2t - 6} \)
5. \( \boxed{9a - 30} \)
6. \( \boxed{21m + 14} \)
7. \( \boxed{10h + 28} \)
8. \( \boxed{9c + 5} \)
9. \( \boxed{18y + 11} \)
10. \( \boxed{15d - 12} \)

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These are the simplified forms of the given algebraic expressions. Each step follows the principles of the distributive property and combining like terms.