Distributive Property Worksheets with Answer Key - Free Printable

Let’s solve each problem step by step using the distributive property. That means we multiply the number outside the parentheses by each term inside, then combine like terms.

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Problem 1: -2(-4x + 5) + 6x

Step 1: Distribute -2 to both terms inside the parentheses:
-2 × (-4x) = 8x
-2 × 5 = -10
So now we have: 8x - 10 + 6x

Step 2: Combine like terms (8x + 6x):
8x + 6x = 14x
Final expression: 14x - 10

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Problem 2: 7x + 3(-2x + 3)

Step 1: Distribute 3:
3 × (-2x) = -6x
3 × 3 = 9
Now: 7x - 6x + 9

Step 2: Combine like terms (7x - 6x):
7x - 6x = x
Final expression: x + 9

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Problem 3: 5(-3x + 7) + 5(x - 1)

Step 1: Distribute 5 in both parts:
5 × (-3x) = -15x
5 × 7 = 35
5 × x = 5x
5 × (-1) = -5
Now: -15x + 35 + 5x - 5

Step 2: Combine like terms:
-15x + 5x = -10x
35 - 5 = 30
Final expression: -10x + 30

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Problem 4: -9(1 - 10x) - 2(3x + 9)

Step 1: Distribute -9 and -2:
-9 × 1 = -9
-9 × (-10x) = 90x
-2 × 3x = -6x
-2 × 9 = -18
Now: -9 + 90x - 6x - 18

Step 2: Combine like terms:
90x - 6x = 84x
-9 - 18 = -27
Final expression: 84x - 27

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Problem 5: 4(2m + 3) + 6m + 5

Step 1: Distribute 4:
4 × 2m = 8m
4 × 3 = 12
Now: 8m + 12 + 6m + 5

Step 2: Combine like terms:
8m + 6m = 14m
12 + 5 = 17
Final expression: 14m + 17

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Problem 6: 6y - (y + 5y) + 3y

First, simplify inside the parentheses:
y + 5y = 6y
Now: 6y - 6y + 3y

Combine like terms:
6y - 6y = 0
0 + 3y = 3y
Final expression: 3y

*(Note: The minus sign before the parentheses applies to everything inside — so it’s like multiplying by -1.)*

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Problem 7: 7 - 8(-2 - 5x)

Step 1: Distribute -8:
-8 × (-2) = 16
-8 × (-5x) = 40x
Now: 7 + 16 + 40x

Step 2: Combine constants:
7 + 16 = 23
Final expression: 40x + 23

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Problem 8: -9x(-9 + 6x) - 5x(7 + 4x)

Step 1: Distribute -9x and -5x:
-9x × (-9) = 81x
-9x × 6x = -54x²
-5x × 7 = -35x
-5x × 4x = -20x²
Now: 81x - 54x² - 35x - 20x²

Step 2: Combine like terms:
For x² terms: -54x² - 20x² = -74x²
For x terms: 81x - 35x = 46x
Final expression: -74x² + 46x

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Problem 9: -p - 5(-6 - 7p)

Step 1: Distribute -5:
-5 × (-6) = 30
-5 × (-7p) = 35p
Now: -p + 30 + 35p

Step 2: Combine like terms:
-p + 35p = 34p
Final expression: 34p + 30

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Problem 10: -4(1 - 8x) - 9(-10x - 1)

Step 1: Distribute -4 and -9:
-4 × 1 = -4
-4 × (-8x) = 32x
-9 × (-10x) = 90x
-9 × (-1) = 9
Now: -4 + 32x + 90x + 9

Step 2: Combine like terms:
32x + 90x = 122x
-4 + 9 = 5
Final expression: 122x + 5

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Final Answer:

1. 14x - 10
2. x + 9
3. -10x + 30
4. 84x - 27
5. 14m + 17
6. 3y
7. 40x + 23
8. -74x² + 46x
9. 34p + 30
10. 122x + 5