Sure! Let’s simplify each of the 10 algebraic expressions step by step. The goal is to
distribute any numbers outside parentheses and then
combine like terms if possible.
---
1) -3(9 + 6w) + 8
- Distribute -3:
→ -3 × 9 = -27
→ -3 × 6w = -18w
So:
-27 - 18w + 8
- Combine constants: -27 + 8 = -19
→ Final answer:
-18w - 19
---
2) 4(-5y - 9)
- Distribute 4:
→ 4 × -5y = -20y
→ 4 × -9 = -36
→ Final answer:
-20y - 36
---
3) 9(-5 + 3c)
- Distribute 9:
→ 9 × -5 = -45
→ 9 × 3c = 27c
→ Final answer:
27c - 45
---
4) -3(6 - 5r)
- Distribute -3:
→ -3 × 6 = -18
→ -3 × -5r = +15r
→ Final answer:
15r - 18
---
5) 8(-9p - 2) + 7
- Distribute 8:
→ 8 × -9p = -72p
→ 8 × -2 = -16
So:
-72p - 16 + 7
- Combine constants: -16 + 7 = -9
→ Final answer:
-72p - 9
---
6) 2(-4 + 8h)
- Distribute 2:
→ 2 × -4 = -8
→ 2 × 8h = 16h
→ Final answer:
16h - 8
---
7) -8(-3 + 6w) - 7w
- Distribute -8:
→ -8 × -3 = +24
→ -8 × 6w = -48w
So:
24 - 48w - 7w
- Combine like terms: -48w - 7w = -55w
→ Final answer:
-55w + 24
---
8) 7(-9r - 5)
- Distribute 7:
→ 7 × -9r = -63r
→ 7 × -5 = -35
→ Final answer:
-63r - 35
---
9) -6s - 7(2 + 9s)
- Distribute -7:
→ -7 × 2 = -14
→ -7 × 9s = -63s
So:
-6s - 14 - 63s
- Combine like terms: -6s - 63s = -69s
→ Final answer:
-69s - 14
---
10) -6 + 4(-9y + 8)
- Distribute 4:
→ 4 × -9y = -36y
→ 4 × 8 = 32
So:
-6 - 36y + 32
- Combine constants: -6 + 32 = 26
→ Final answer:
-36y + 26
---
##
✔ Final Answers:
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
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Let me know if you’d like to see a video explanation or practice more problems like these!
Parent Tip: Review the logic above to help your child master the concept of adding linear expressions worksheet.
