Algebra worksheet with distributive property exercises and a fun riddle answer key.

Let’s solve each problem step by step. We’ll use the distributive property (multiply the number outside the parentheses by each term inside) and then combine like terms if needed.

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1. 5(2x + 3)
= 5×2x + 5×3 = 10x + 15 → Look for this in answers: O. 10x + 15

2. 8(3m + 4)
= 8×3m + 8×4 = 24m + 32 → E. 24m + 32

3. 4(3 - 2y)
= 4×3 - 4×2y = 12 - 8y → B. 12 - 8y

4. (8 + 3n)(6)
Same as 6(8 + 3n) = 6×8 + 6×3n = 48 + 18n → A. 48 + 18n

5. 6(2x - 3)
= 6×2x - 6×3 = 12x - 18 → Y. 12x - 18

6. 9(2x + 6y)
= 9×2x + 9×6y = 18x + 54y → E. 18x + 54y *(Note: E is used twice — that’s okay, it’s a worksheet)*

7. 7(x + 2y)
= 7×x + 7×2y = 7x + 14y → T. 7x + 14y

8. 8(4x - 3y)
= 8×4x - 8×3y = 32x - 24y → O. 32x - 24y *(Again, O is reused — fine)*

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Now problems 9–16: Distribute AND combine like terms.

9. 2(3x + 4) + 6
= 2×3x + 2×4 + 6 = 6x + 8 + 6 = 6x + 14 → E. 6x + 14

10. 3(x + 4) + 2x
= 3×x + 3×4 + 2x = 3x + 12 + 2x = (3x + 2x) + 12 = 5x + 12 → S. 5x + 12

11. 4(2x + 3y) + 7x
= 4×2x + 4×3y + 7x = 8x + 12y + 7x = (8x + 7x) + 12y = 15x + 12y → H. 15x + 12y

12. 8(3 - 2f) + 3
= 8×3 - 8×2f + 3 = 24 - 16f + 3 = (24 + 3) - 16f = 27 - 16f → N. 27 - 16f

13. (9n + 6)(4) + 3n
= 4×9n + 4×6 + 3n = 36n + 24 + 3n = (36n + 3n) + 24 = 39n + 24 → V. 39n + 24

14. 5m + 7(2 + 8m)
First distribute: 7×2 + 7×8m = 14 + 56m
Then add 5m: 5m + 14 + 56m = (5m + 56m) + 14 = 61m + 14 → H. 14 + 61m *(same as 61m + 14)*

15. 6(x + y) + x
= 6×x + 6×y + x = 6x + 6y + x = (6x + x) + 6y = 7x + 6y → C. 7x + 6y

16. 3 + 9(2n + 1) + 4n
Distribute first: 9×2n + 9×1 = 18n + 9
Now whole expression: 3 + 18n + 9 + 4n = (18n + 4n) + (3 + 9) = 22n + 12 → H. 22n + 12

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Challenge Problems:

17. 2(5x + 2y) + 3(2y + x)
Distribute both:
2×5x + 2×2y = 10x + 4y
3×2y + 3×x = 6y + 3x
Now combine all: 10x + 4y + 6y + 3x = (10x + 3x) + (4y + 6y) = 13x + 10y → M. 13x + 10y

18. 2(7 - 3x) + 6(3 + 2y) + 3y + 2
Distribute:
2×7 - 2×3x = 14 - 6x
6×3 + 6×2y = 18 + 12y
Now put all together:
14 - 6x + 18 + 12y + 3y + 2
Combine constants: 14 + 18 + 2 = 34
Combine y terms: 12y + 3y = 15y
So: 34 - 6x + 15y → Y. 34 - 6x + 15y

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Final Answer:

1. O
2. E
3. B
4. A
5. Y
6. E
7. T
8. O
9. E
10. S
11. H
12. N
13. V
14. H
15. C
16. H
17. M
18. Y