Math worksheet practicing the distributive property with 22 problems involving simplifying expressions with parentheses.

Problem: Simplify each expression using the distributive property.

The distributive property states that for any numbers \( a \), \( b \), and \( c \):
\[
a(b + c) = ab + ac
\]
This property allows us to distribute the multiplication over addition or subtraction.

Let's solve each expression step by step.

---

#### 1) \( 13(15 + 4x) \)
\[
13(15 + 4x) = 13 \cdot 15 + 13 \cdot 4x = 195 + 52x
\]
Answer: \( 195 + 52x \)

---

#### 2) \( -13(13 + 3x) \)
\[
-13(13 + 3x) = -13 \cdot 13 + (-13) \cdot 3x = -169 - 39x
\]
Answer: \( -169 - 39x \)

---

#### 3) \( -5(6 + 8x) \)
\[
-5(6 + 8x) = -5 \cdot 6 + (-5) \cdot 8x = -30 - 40x
\]
Answer: \( -30 - 40x \)

---

#### 4) \( -15(17 - 3x) \)
\[
-15(17 - 3x) = -15 \cdot 17 + (-15) \cdot (-3x) = -255 + 45x
\]
Answer: \( -255 + 45x \)

---

#### 5) \( -(-19 - 2x) \)
\[
-(-19 - 2x) = -1 \cdot (-19) + (-1) \cdot (-2x) = 19 + 2x
\]
Answer: \( 19 + 2x \)

---

#### 6) \( -(7 - 4x) \)
\[
-(7 - 4x) = -1 \cdot 7 + (-1) \cdot (-4x) = -7 + 4x
\]
Answer: \( -7 + 4x \)

---

#### 7) \( -3(9 - 7x) \)
\[
-3(9 - 7x) = -3 \cdot 9 + (-3) \cdot (-7x) = -27 + 21x
\]
Answer: \( -27 + 21x \)

---

#### 8) \( 20(20 + 2x) \)
\[
20(20 + 2x) = 20 \cdot 20 + 20 \cdot 2x = 400 + 40x
\]
Answer: \( 400 + 40x \)

---

#### 9) \( -15(20 + 8x) \)
\[
-15(20 + 8x) = -15 \cdot 20 + (-15) \cdot 8x = -300 - 120x
\]
Answer: \( -300 - 120x \)

---

#### 10) \( -6(3 - 8x) \)
\[
-6(3 - 8x) = -6 \cdot 3 + (-6) \cdot (-8x) = -18 + 48x
\]
Answer: \( -18 + 48x \)

---

#### 11) \( -17(19 - 3x) \)
\[
-17(19 - 3x) = -17 \cdot 19 + (-17) \cdot (-3x) = -323 + 51x
\]
Answer: \( -323 + 51x \)

---

#### 12) \( -(-3 - 6x) \)
\[
-(-3 - 6x) = -1 \cdot (-3) + (-1) \cdot (-6x) = 3 + 6x
\]
Answer: \( 3 + 6x \)

---

#### 13) \( -5(5 + 7x) \)
\[
-5(5 + 7x) = -5 \cdot 5 + (-5) \cdot 7x = -25 - 35x
\]
Answer: \( -25 - 35x \)

---

#### 14) \( 12(18 + 8x) \)
\[
12(18 + 8x) = 12 \cdot 18 + 12 \cdot 8x = 216 + 96x
\]
Answer: \( 216 + 96x \)

---

#### 15) \( -(-5 - 3x) \)
\[
-(-5 - 3x) = -1 \cdot (-5) + (-1) \cdot (-3x) = 5 + 3x
\]
Answer: \( 5 + 3x \)

---

#### 16) \( -(-18 - 7x) \)
\[
-(-18 - 7x) = -1 \cdot (-18) + (-1) \cdot (-7x) = 18 + 7x
\]
Answer: \( 18 + 7x \)

---

#### 17) \( -10(10 + 3x) \)
\[
-10(10 + 3x) = -10 \cdot 10 + (-10) \cdot 3x = -100 - 30x
\]
Answer: \( -100 - 30x \)

---

#### 18) \( -(13 - 3x) \)
\[
-(13 - 3x) = -1 \cdot 13 + (-1) \cdot (-3x) = -13 + 3x
\]
Answer: \( -13 + 3x \)

---

#### 19) \( 2(7 + 7x) \)
\[
2(7 + 7x) = 2 \cdot 7 + 2 \cdot 7x = 14 + 14x
\]
Answer: \( 14 + 14x \)

---

#### 20) \( -5(12 - 8x) \)
\[
-5(12 - 8x) = -5 \cdot 12 + (-5) \cdot (-8x) = -60 + 40x
\]
Answer: \( -60 + 40x \)

---

#### 21) \( -(-12 - 6x) \)
\[
-(-12 - 6x) = -1 \cdot (-12) + (-1) \cdot (-6x) = 12 + 6x
\]
Answer: \( 12 + 6x \)

---

#### 22) \( -(-20 - 3x) \)
\[
-(-20 - 3x) = -1 \cdot (-20) + (-1) \cdot (-3x) = 20 + 3x
\]
Answer: \( 20 + 3x \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 195 + 52x \\
2) & -169 - 39x \\
3) & -30 - 40x \\
4) & -255 + 45x \\
5) & 19 + 2x \\
6) & -7 + 4x \\
7) & -27 + 21x \\
8) & 400 + 40x \\
9) & -300 - 120x \\
10) & -18 + 48x \\
11) & -323 + 51x \\
12) & 3 + 6x \\
13) & -25 - 35x \\
14) & 216 + 96x \\
15) & 5 + 3x \\
16) & 18 + 7x \\
17) & -100 - 30x \\
18) & -13 + 3x \\
19) & 14 + 14x \\
20) & -60 + 40x \\
21) & 12 + 6x \\
22) & 20 + 3x \\
\end{array}
}
\]