Using the Distributive Property (Answers Do Not Include Exponents) (A) - Free Printable

You're working on Distributive Property (A) — a foundational algebra skill. The distributive property says:

> a(b + c) = ab + ac
> or more generally,
> a(b ± c) = ab ± ac

This means you multiply the term *outside* the parentheses by *each term inside* the parentheses, and then combine like terms if needed.

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Let’s solve each expression one by one, applying the distributive property carefully.

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Left Column:

1. 2(4 + 9w)
= 2×4 + 2×9w
= 8 + 18w

2. -4(-4d - 5)
= (-4)×(-4d) + (-4)×(-5)
= 16d + 20

3. 2(3v - 8)
= 2×3v - 2×8
= 6v - 16

4. 4(-6z + 4)
= 4×(-6z) + 4×4
= -24z + 16

5. (-5d + 1)(-2)
= (-2)×(-5d) + (-2)×1
= 10d - 2

6. 2(-5 - 7j)
= 2×(-5) + 2×(-7j)
= -10 - 14j

7. -3(3 - 8j)
= (-3)×3 + (-3)×(-8j)
= -9 + 24j

8. -8(2 + 9v)
= (-8)×2 + (-8)×9v
= -16 - 72v

9. (-5f + 8)4
= 4×(-5f) + 4×8
= -20f + 32

10. -(6 - 4p)
This is the same as -1(6 - 4p)
= (-1)×6 + (-1)×(-4p)
= -6 + 4p or 4p - 6

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Right Column:

1. -8(6x + 3)
= (-8)×6x + (-8)×3
= -48x - 24

2. -6(8p + 3)
= (-6)×8p + (-6)×3
= -48p - 18

3. (2 - 5m)(-5)
= (-5)×2 + (-5)×(-5m)
= -10 + 25m

4. -9(n - 4)
= (-9)×n + (-9)×(-4)
= -9n + 36

5. -4(9k + 9)
= (-4)×9k + (-4)×9
= -36k - 36

6. (3b - 2)(-3)
= (-3)×3b + (-3)×(-2)
= -9b + 6

7. -(-5 - 3v)
This is -1(-5 - 3v)
= (-1)×(-5) + (-1)×(-3v)
= 5 + 3v

8. -9(8 - 2h)
= (-9)×8 + (-9)×(-2h)
= -72 + 18h

9. (7x - 8)(-1)
= (-1)×7x + (-1)×(-8)
= -7x + 8

10. 9(8 + 5t)
= 9×8 + 9×5t
= 72 + 45t

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## ✔ Final Answer Key:

Left Column:

1. 8 + 18w
2. 16d + 20
3. 6v - 16
4. -24z + 16
5. 10d - 2
6. -10 - 14j
7. -9 + 24j
8. -16 - 72v
9. -20f + 32
10. 4p - 6

Right Column:

1. -48x - 24
2. -48p - 18
3. -10 + 25m
4. -9n + 36
5. -36k - 36
6. -9b + 6
7. 5 + 3v
8. -72 + 18h
9. -7x + 8
10. 72 + 45t

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💡 Tip: Always watch your signs! Multiplying two negatives gives a positive. A negative times a positive gives a negative.

Let me know if you want to check your work or need help with another worksheet!