Let's solve each problem step by step using the
distributive property and combining like terms. The distributive property states:
> $ a(b + c) = ab + ac $
We'll simplify each expression accordingly.
---
1. $ 8(x + 4) $
Distribute 8 to both terms inside the parentheses:
$$
8 \cdot x + 8 \cdot 4 = 8x + 32
$$
✔ Answer: $ 8x + 32 $
---
2. $ (4a - 1)2 $
This is the same as $ 2(4a - 1) $. Distribute 2:
$$
2 \cdot 4a - 2 \cdot 1 = 8a - 2
$$
✔ Answer: $ 8a - 2 $
---
3. $ -2(6x - 5) $
Distribute $-2$ to both terms:
$$
-2 \cdot 6x + (-2) \cdot (-5) = -12x + 10
$$
✔ Answer: $ -12x + 10 $
---
4. $ 2(3x - 1) + x $
First, distribute 2:
$$
2 \cdot 3x - 2 \cdot 1 = 6x - 2
$$
Now add $ x $:
$$
6x - 2 + x = 7x - 2
$$
✔ Answer: $ 7x - 2 $
---
5. $ 6r + 2(r + 4) $
Distribute 2:
$$
6r + 2r + 8 = 8r + 8
$$
✔ Answer: $ 8r + 8 $
---
6. $ 12y - (y - 7) $
Distribute the negative sign (like multiplying by $-1$):
$$
12y - y + 7 = 11y + 7
$$
✔ Answer: $ 11y + 7 $
---
7. $ 3(m + 5) - 10 $
Distribute 3:
$$
3m + 15 - 10 = 3m + 5
$$
✔ Answer: $ 3m + 5 $
---
8. $ -4(x + 2) + 2x $
Distribute $-4$:
$$
-4x - 8 + 2x = (-4x + 2x) - 8 = -2x - 8
$$
✔ Answer: $ -2x - 8 $
---
9. $ 7(w - 5) + 3w $
Distribute 7:
$$
7w - 35 + 3w = (7w + 3w) - 35 = 10w - 35
$$
✔ Answer: $ 10w - 35 $
---
10. $ 5(x + 2) - 3(x - 4) $
Distribute both:
$$
5x + 10 - 3x + 12 \quad \text{(note: } -3 \cdot (-4) = +12\text{)}
$$
Combine like terms:
$$
(5x - 3x) + (10 + 12) = 2x + 22
$$
✔ Answer: $ 2x + 22 $
---
11. $ -2(c - 2) + 4(c - 1) $
Distribute:
$$
-2c + 4 + 4c - 4
$$
Combine like terms:
$$
(-2c + 4c) + (4 - 4) = 2c + 0 = 2c
$$
✔ Answer: $ 2c $
---
12. $ 3(b + 5) - (b - 2) $
Distribute:
$$
3b + 15 - b + 2 \quad \text{(distribute negative sign)}
$$
Combine:
$$
(3b - b) + (15 + 2) = 2b + 17
$$
✔ Answer: $ 2b + 17 $
---
13. $ 4(x - 2) + 3(x + 9) $
Distribute:
$$
4x - 8 + 3x + 27
$$
Combine:
$$
(4x + 3x) + (-8 + 27) = 7x + 19
$$
✔ Answer: $ 7x + 19 $
---
✔ Final Answers Summary:
1. $ 8x + 32 $
2. $ 8a - 2 $
3. $ -12x + 10 $
4. $ 7x - 2 $
5. $ 8r + 8 $
6. $ 11y + 7 $
7. $ 3m + 5 $
8. $ -2x - 8 $
9. $ 10w - 35 $
10. $ 2x + 22 $
11. $ 2c $
12. $ 2b + 17 $
13. $ 7x + 19 $
Let me know if you'd like these written in a formatted worksheet style!
Parent Tip: Review the logic above to help your child master the concept of 11th grade algebra 2 worksheet.
