Distributive Property Practice worksheet for Algebra 1 students.

Let's solve each expression using the distributive property, which states:

> $ a(b + c) = ab + ac $

This means we multiply the term outside the parentheses by each term inside the parentheses.

---

1) $ 7(x - 4) $

Distribute 7 to both $ x $ and $ -4 $:
$$
7 \cdot x = 7x \\
7 \cdot (-4) = -28
$$
So:
$$
7(x - 4) = 7x - 28
$$

---

2) $ -9(9 - 10n) $

Distribute $-9$ to both $ 9 $ and $ -10n $:
$$
-9 \cdot 9 = -81 \\
-9 \cdot (-10n) = +90n
$$
So:
$$
-9(9 - 10n) = -81 + 90n \quad \text{or} \quad 90n - 81
$$

---

3) $ 4(8 + n) $

Distribute 4:
$$
4 \cdot 8 = 32 \\
4 \cdot n = 4n
$$
So:
$$
4(8 + n) = 32 + 4n
$$

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4) $ -(4m - 4) $

This is the same as multiplying by $-1$:
$$
-1 \cdot 4m = -4m \\
-1 \cdot (-4) = +4
$$
So:
$$
-(4m - 4) = -4m + 4
$$

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5) $ 2(v + 2) $

Distribute 2:
$$
2 \cdot v = 2v \\
2 \cdot 2 = 4
$$
So:
$$
2(v + 2) = 2v + 4
$$

---

6) $ 4(x - 7) $

Distribute 4:
$$
4 \cdot x = 4x \\
4 \cdot (-7) = -28
$$
So:
$$
4(x - 7) = 4x - 28
$$

---

7) $ -(p - 4) $

Multiply by $-1$:
$$
-1 \cdot p = -p \\
-1 \cdot (-4) = +4
$$
So:
$$
-(p - 4) = -p + 4
$$

---

8) $ 6(m + 8) $

Distribute 6:
$$
6 \cdot m = 6m \\
6 \cdot 8 = 48
$$
So:
$$
6(m + 8) = 6m + 48
$$

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9) $ -9(7n - 6) $

Distribute $-9$:
$$
-9 \cdot 7n = -63n \\
-9 \cdot (-6) = +54
$$
So:
$$
-9(7n - 6) = -63n + 54
$$

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10) $ -6(b - 3) $

Distribute $-6$:
$$
-6 \cdot b = -6b \\
-6 \cdot (-3) = +18
$$
So:
$$
-6(b - 3) = -6b + 18
$$

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✔ Final Answers:

1) $ 7x - 28 $
2) $ 90n - 81 $
3) $ 32 + 4n $
4) $ -4m + 4 $
5) $ 2v + 4 $
6) $ 4x - 28 $
7) $ -p + 4 $
8) $ 6m + 48 $
9) $ -63n + 54 $
10) $ -6b + 18 $

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🔍 Summary of Key Concepts:

- The distributive property allows us to eliminate parentheses by multiplying.
- When distributing a negative number, be careful with signs: negative × negative = positive, negative × positive = negative.
- Always distribute to every term inside the parentheses.

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