Practice worksheet on the distributive property for simplifying algebraic expressions.

Let’s solve each problem step by step using the Distributive Property and then simplify where possible.

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What is the Distributive Property?

It says:
> a(b + c) = ab + ac
or
> a(b - c) = ab - ac

We “distribute” the number outside the parentheses to each term inside.

Also, when simplifying expressions with variables, we combine like terms — terms that have the same variable part (same letter and same exponent).

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## Let’s go one by one:

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1. 5(2x + 7)
→ Distribute 5 to both terms:
5 × 2x = 10x
5 × 7 = 35
✔ Final: 10x + 35

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2. 8(x - 6)
→ 8 × x = 8x
8 × (-6) = -48
✔ Final: 8x - 48

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3. 2(m + n)
→ 2 × m = 2m
2 × n = 2n
✔ Final: 2m + 2n

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4. -3(y - 3y) ← Wait! Inside parentheses: y - 3y = -2y
So it becomes: -3(-2y) = 6y
But let’s do it step by step as written:

Actually, better to simplify inside first if possible.

Original: -3(y - 3y)
Inside: y - 3y = -2y
Then: -3 × (-2y) = +6y

✔ Final: 6y

*(Note: If you distribute without simplifying first: -3×y = -3y; -3×(-3y)=+9y → -3y + 9y = 6y — same answer.)*

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5. 5a + 4a → Like terms! Both are “a” terms.
5a + 4a = (5+4)a = 9a

✔ Final: 9a

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6. 12y - y → Same as 12y - 1y = (12-1)y = 11y

✔ Final: 11y

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7. 4ab + 4b² → These are NOT like terms. One has “ab”, other has “b²”. Can’t combine.

✔ Final: 4ab + 4b² *(already simplified)*

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8. 7c³ + 4c³ → Like terms! Both c³.
7 + 4 = 11 → 11c³

✔ Final: 11c³

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9. 14m - 10m → 14 - 10 = 4 → 4m

✔ Final: 4m

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10. 3p - 5p → 3 - 5 = -2 → -2p

✔ Final: -2p

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11. 15z² + 10z² → 15 + 10 = 25 → 25z²

✔ Final: 25z²

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12. 8t³ - 10t³ → 8 - 10 = -2 → -2t³

✔ Final: -2t³

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13. 6x + 2y + 2x → Combine like terms: 6x + 2x = 8x; 2y stays.
→ 8x + 2y

✔ Final: 8x + 2y

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14. k + 8 + k + 4 → Group: k + k = 2k; 8 + 4 = 12
→ 2k + 12

✔ Final: 2k + 12

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15. 5y + 2x + x → 2x + x = 3x; 5y stays
→ 5y + 3x (or 3x + 5y — order doesn’t matter)

✔ Final: 3x + 5y

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16. 3x + 5y - 3x → 3x - 3x = 0; left with 5y
→ 5y

✔ Final: 5y

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17. 13x + 5x + 2xy → 13x + 5x = 18x; 2xy stays (different term)
→ 18x + 2xy

✔ Final: 18x + 2xy

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18. 5a + 11a + 2a → All like terms: 5 + 11 + 2 = 18 → 18a

✔ Final: 18a

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19. 7m + 2m + 3m → 7 + 2 + 3 = 12 → 12m

✔ Final: 12m

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20. m + 13m + 6m → 1 + 13 + 6 = 20 → 20m

✔ Final: 20m

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21. 4a² + b² + a² + 3b² → Group:
a² terms: 4a² + a² = 5a²
b² terms: b² + 3b² = 4b²
→ 5a² + 4b²

✔ Final: 5a² + 4b²

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22. 3a + (1/2)b → No like terms. Already simplified.

✔ Final: 3a + (1/2)b

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23. (1/2)x + (1/3)x + (1/6)x → Need common denominator to add fractions.

LCM of 2, 3, 6 is 6.

Convert:
- (1/2)x = (3/6)x
- (1/3)x = (2/6)x
- (1/6)x = (1/6)x

Add: 3/6 + 2/6 + 1/6 = 6/6 = 1 → 1x or just x

✔ Final: x

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24. 5a + (3/4)a → Convert 5 to fourths: 5 = 20/4
So: 20/4 a + 3/4 a = 23/4 a → (23/4)a or 5¾a

Either form is fine, but fractional is exact.

✔ Final: (23/4)a

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25. 15a + 3a + 2(a + 1) → First, distribute the 2:
2(a + 1) = 2a + 2

Now expression becomes:
15a + 3a + 2a + 2

Combine like terms:
15a + 3a + 2a = 20a
Plus 2 → 20a + 2

✔ Final: 20a + 2

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## ✔ FINAL ANSWERS LIST:

1. 10x + 35
2. 8x - 48
3. 2m + 2n
4. 6y
5. 9a
6. 11y
7. 4ab + 4b²
8. 11c³
9. 4m
10. -2p
11. 25z²
12. -2t³
13. 8x + 2y
14. 2k + 12
15. 3x + 5y
16. 5y
17. 18x + 2xy
18. 18a
19. 12m
20. 20m
21. 5a² + 4b²
22. 3a + (1/2)b
23. x
24. (23/4)a
25. 20a + 2

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Final Answer:
1. 10x + 35
2. 8x - 48
3. 2m + 2n
4. 6y
5. 9a
6. 11y
7. 4ab + 4b²
8. 11c³
9. 4m
10. -2p
11. 25z²
12. -2t³
13. 8x + 2y
14. 2k + 12
15. 3x + 5y
16. 5y
17. 18x + 2xy
18. 18a
19. 12m
20. 20m
21. 5a² + 4b²
22. 3a + \frac{1}{2}b
23. x
24. \frac{23}{4}a
25. 20a + 2