Algebraic Expressions Worksheets | Distributive Property Worksheets - Free Printable

Sure! Let’s solve each of the 10 problems step by step. The goal is to simplify algebraic expressions by using the distributive property and then combining like terms where possible.

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Problem 1: -3(9 + 6w) + 8

Step 1: Distribute -3 to both terms inside the parentheses:
-3 × 9 = -27
-3 × 6w = -18w

So we get:
→ -27 - 18w + 8

Step 2: Combine constant terms (-27 + 8):
→ -19 - 18w

✔ Final Answer: -18w - 19

*(We usually write variables first, but either order is acceptable unless specified.)*

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Problem 2: 4(-5y - 9)

Step 1: Distribute 4:
4 × -5y = -20y
4 × -9 = -36

✔ Final Answer: -20y - 36

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Problem 3: 9(-5 + 3c)

Step 1: Distribute 9:
9 × -5 = -45
9 × 3c = 27c

✔ Final Answer: 27c - 45

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Problem 4: -3(6 - 5r)

Step 1: Distribute -3:
-3 × 6 = -18
-3 × -5r = +15r *(negative × negative = positive)*

✔ Final Answer: 15r - 18

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Problem 5: 8(-9p - 2) + 7

Step 1: Distribute 8:
8 × -9p = -72p
8 × -2 = -16

Expression becomes:
→ -72p - 16 + 7

Step 2: Combine constants: -16 + 7 = -9

✔ Final Answer: -72p - 9

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Problem 6: 2(-4 + 8h)

Step 1: Distribute 2:
2 × -4 = -8
2 × 8h = 16h

✔ Final Answer: 16h - 8

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Problem 7: -8(-3 + 6w) - 7w

Step 1: Distribute -8:
-8 × -3 = +24
-8 × 6w = -48w

Expression becomes:
→ 24 - 48w - 7w

Step 2: Combine like terms (-48w - 7w = -55w)

✔ Final Answer: -55w + 24 or 24 - 55w

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Problem 8: 7(-9r - 5)

Step 1: Distribute 7:
7 × -9r = -63r
7 × -5 = -35

✔ Final Answer: -63r - 35

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Problem 9: -6s - 7(2 + 9s)

Step 1: Distribute -7:
-7 × 2 = -14
-7 × 9s = -63s

Expression becomes:
→ -6s - 14 - 63s

Step 2: Combine like terms (-6s - 63s = -69s)

✔ Final Answer: -69s - 14

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Problem 10: -6 + 4(-9y + 8)

Step 1: Distribute 4:
4 × -9y = -36y
4 × 8 = 32

Expression becomes:
→ -6 - 36y + 32

Step 2: Combine constants: -6 + 32 = 26

✔ Final Answer: -36y + 26

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## ✔ Final Answers Summary:

1) -18w - 19
2) -20y - 36
3) 27c - 45
4) 15r - 18
5) -72p - 9
6) 16h - 8
7) -55w + 24
8) -63r - 35
9) -69s - 14
10) -36y + 26

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Let me know if you’d like a printable version or want to check your work against these answers! 😊