Using the Distributive Property - Kuta Software - Free Printable

Let's solve each expression using the Distributive Property, which states:

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

We'll apply this property to simplify each expression. Let's go through them one by one.

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1) $-6(a + 8)$

Distribute $-6$ to both terms inside the parentheses:

$$
-6 \cdot a + (-6) \cdot 8 = -6a - 48
$$

✔ Answer: $-6a - 48$

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2) $4(1 + 9x)$

Distribute $4$:

$$
4 \cdot 1 + 4 \cdot 9x = 4 + 36x
$$

✔ Answer: $4 + 36x$

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3) $6(-5n + 7)$

Distribute $6$:

$$
6 \cdot (-5n) + 6 \cdot 7 = -30n + 42
$$

✔ Answer: $-30n + 42$

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4) $(9m + 10) - 2$

Wait — this is not a distributive problem in the same way. There’s no multiplication over addition here, just subtraction.

But we can interpret it as:

$$
(9m + 10) - 2 = 9m + 10 - 2 = 9m + 8
$$

✔ Answer: $9m + 8$

(Note: This doesn't involve distribution unless there was a typo and it was meant to be something like $-2(9m + 10)$, but as written, it's just simplifying.)

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5) $(-4 - 3n) - 8$

Again, no distribution needed — just combine like terms:

$$
-4 - 3n - 8 = -3n - 12
$$

✔ Answer: $-3n - 12$

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6) $8(-b - 4)$

Distribute $8$:

$$
8 \cdot (-b) + 8 \cdot (-4) = -8b - 32
$$

✔ Answer: $-8b - 32$

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7) $(1 - 7n) - 5$

Simplify by combining constants:

$$
1 - 7n - 5 = -7n - 4
$$

✔ Answer: $-7n - 4$

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8) $-6(x + 4)$

Distribute $-6$:

$$
-6 \cdot x + (-6) \cdot 4 = -6x - 24
$$

✔ Answer: $-6x - 24$

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9) $5(3n - 6)$

Distribute $5$:

$$
5 \cdot 3n + 5 \cdot (-6) = 15n - 30
$$

✔ Answer: $15n - 30$

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10) $(-6p + 7) \cdot -4$

This means: $-4(-6p + 7)$

Distribute $-4$:

$$
-4 \cdot (-6p) + (-4) \cdot 7 = 24p - 28
$$

✔ Answer: $24p - 28$

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11) $5(b - 1)$

Distribute $5$:

$$
5 \cdot b + 5 \cdot (-1) = 5b - 5
$$

✔ Answer: $5b - 5$

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12) $(x + 9) - 5$

Combine like terms:

$$
x + 9 - 5 = x + 4
$$

✔ Answer: $x + 4$

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✔ Final Answers:

1) $-6a - 48$
2) $4 + 36x$
3) $-30n + 42$
4) $9m + 8$
5) $-3n - 12$
6) $-8b - 32$
7) $-7n - 4$
8) $-6x - 24$
9) $15n - 30$
10) $24p - 28$
11) $5b - 5$
12) $x + 4$

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