To solve these problems, we use the
distributive property. This means multiplying the number outside the parentheses by each term inside the parentheses.
Let’s go through each one step by step:
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1. 2(4 + 9w)
→ 2 × 4 = 8
→ 2 × 9w = 18w
✔ Final:
8 + 18w
---
2. -8(6x + 3)
→ -8 × 6x = -48x
→ -8 × 3 = -24
✔ Final:
-48x - 24
---
3. -4(-4d - 5)
→ -4 × -4d = +16d
→ -4 × -5 = +20
✔ Final:
16d + 20
---
4. -6(8p + 3)
→ -6 × 8p = -48p
→ -6 × 3 = -18
✔ Final:
-48p - 18
---
5. 2(3v - 8)
→ 2 × 3v = 6v
→ 2 × -8 = -16
✔ Final:
6v - 16
---
6. (2 - 5m)(-5)
→ Think of it as -5 × (2 - 5m)
→ -5 × 2 = -10
→ -5 × -5m = +25m
✔ Final:
-10 + 25m or
25m - 10
---
7. 4(-6z + 4)
→ 4 × -6z = -24z
→ 4 × 4 = 16
✔ Final:
-24z + 16
---
8. -9(n - 4)
→ -9 × n = -9n
→ -9 × -4 = +36
✔ Final:
-9n + 36
---
9. (-5d + 1)(-2)
→ Multiply each term by -2
→ -2 × -5d = +10d
→ -2 × 1 = -2
✔ Final:
10d - 2
---
10. -4(9k + 9)
→ -4 × 9k = -36k
→ -4 × 9 = -36
✔ Final:
-36k - 36
---
11. 2(-5 - 7j)
→ 2 × -5 = -10
→ 2 × -7j = -14j
✔ Final:
-10 - 14j
---
12. (3b - 2)(-3)
→ -3 × 3b = -9b
→ -3 × -2 = +6
✔ Final:
-9b + 6
---
13. -3(3 - 8j)
→ -3 × 3 = -9
→ -3 × -8j = +24j
✔ Final:
-9 + 24j or
24j - 9
---
14. -(5 - 3v)
→ This is like multiplying by -1
→ -1 × 5 = -5
→ -1 × -3v = +3v
✔ Final:
-5 + 3v or
3v - 5
---
15. -8(2 + 9v)
→ -8 × 2 = -16
→ -8 × 9v = -72v
✔ Final:
-16 - 72v
---
16. -9(8 - 2h)
→ -9 × 8 = -72
→ -9 × -2h = +18h
✔ Final:
-72 + 18h or
18h - 72
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17. (-5f + 8)4
→ Same as 4 × (-5f + 8)
→ 4 × -5f = -20f
→ 4 × 8 = 32
✔ Final:
-20f + 32
---
18. (7x - 8)(-1)
→ -1 × 7x = -7x
→ -1 × -8 = +8
✔ Final:
-7x + 8
---
19. -(6 - 4p)
→ Like multiplying by -1
→ -1 × 6 = -6
→ -1 × -4p = +4p
✔ Final:
-6 + 4p or
4p - 6
---
20. 9(8 + 5t)
→ 9 × 8 = 72
→ 9 × 5t = 45t
✔ Final:
72 + 45t
---
Final Answer:
8 + 18w
-48x - 24
16d + 20
-48p - 18
6v - 16
25m - 10
-24z + 16
-9n + 36
10d - 2
-36k - 36
-10 - 14j
-9b + 6
24j - 9
3v - 5
-16 - 72v
18h - 72
-20f + 32
-7x + 8
4p - 6
72 + 45t
Parent Tip: Review the logic above to help your child master the concept of distributing worksheet.
