Use this worksheet to practice applying the distributive property and combining like terms to simplify algebraic expressions.

Sure! Let’s simplify each of the 10 algebraic expressions step by step. The main technique we’ll use is the Distributive Property:
> a(b + c) = ab + ac
and then combine like terms if needed.

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

Step 1: Distribute -3 to both terms inside the parentheses:
= (-3)(9) + (-3)(6w) + 8
= -27 - 18w + 8

Step 2: Combine like terms (-27 and +8):
= -18w - 19

✔ Final Answer: -18w - 19

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2) 4(-5y - 9)

Step 1: Distribute 4 to both terms:
= (4)(-5y) + (4)(-9)
= -20y - 36

✔ Final Answer: -20y - 36

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3) 9(-5 + 3c)

Step 1: Distribute 9:
= (9)(-5) + (9)(3c)
= -45 + 27c

Step 2: Rearrange (optional, but standard form puts variable first):
= 27c - 45

✔ Final Answer: 27c - 45

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4) -3(6 - 5r)

Step 1: Distribute -3:
= (-3)(6) + (-3)(-5r)
= -18 + 15r

Step 2: Rearrange:
= 15r - 18

✔ Final Answer: 15r - 18

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

Step 1: Distribute 8:
= (8)(-9p) + (8)(-2) + 7
= -72p - 16 + 7

Step 2: Combine constants:
= -72p - 9

✔ Final Answer: -72p - 9

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6) 2(-4 + 8h)

Step 1: Distribute 2:
= (2)(-4) + (2)(8h)
= -8 + 16h

Step 2: Rearrange:
= 16h - 8

✔ Final Answer: 16h - 8

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

Step 1: Distribute -8:
= (-8)(-3) + (-8)(6w) - 7w
= 24 - 48w - 7w

Step 2: Combine like terms (-48w - 7w):
= 24 - 55w

Step 3: Rearrange:
= -55w + 24

✔ Final Answer: -55w + 24

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8) 7(-9r - 5)

Step 1: Distribute 7:
= (7)(-9r) + (7)(-5)
= -63r - 35

✔ Final Answer: -63r - 35

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

Step 1: Distribute -7:
= -6s - [7×2 + 7×9s]
= -6s - (14 + 63s)

Step 2: Distribute the negative sign:
= -6s - 14 - 63s

Step 3: Combine like terms (-6s - 63s):
= -69s - 14

✔ Final Answer: -69s - 14

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

Step 1: Distribute 4:
= -6 + [4×(-9y) + 4×8]
= -6 + (-36y + 32)

Step 2: Remove brackets and rearrange:
= -36y -6 + 32

Step 3: Combine constants:
= -36y + 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

Let me know if you’d like a printable version or to check your own work!