Sure! Let’s solve each problem step by step using the
Distributive Property, which states:
>
a(b + c) = ab + ac
We’ll simplify each expression by distributing the number outside the parentheses to each term inside, then combine like terms if needed.
---
1. 8(x + 4)
Distribute 8 to both x and 4:
= 8·x + 8·4
=
8x + 32
✔ Answer: 8x + 32
---
2. (4a - 1)2
This is the same as
2(4a - 1) — distribute 2:
= 2·4a - 2·1
=
8a - 2
✔ Answer: 8a - 2
---
3. -2(3x - 5)
Distribute -2 to both 3x and -5:
= (-2)·3x + (-2)·(-5)
= -6x + 10
✔ Answer: -6x + 10
---
4. 2(3x - 1) + x
First, distribute 2:
= 2·3x - 2·1 + x
= 6x - 2 + x
Now combine like terms (6x + x):
=
7x - 2
✔ Answer: 7x - 2
---
5. 6r + 2(r + 4)
Distribute 2:
= 6r + 2·r + 2·4
= 6r + 2r + 8
Combine like terms:
=
8r + 8
✔ Answer: 8r + 8
---
6. 12y - (y - 7)
The minus sign before the parentheses means distribute
-1:
= 12y - 1·y + 1·7
= 12y - y + 7
Combine like terms:
=
11y + 7
✔ Answer: 11y + 7
---
7. 3(m + 5) - 10
Distribute 3:
= 3·m + 3·5 - 10
= 3m + 15 - 10
Combine constants:
=
3m + 5
✔ Answer: 3m + 5
---
8. -4(x + 2) + 2x
Distribute -4:
= -4·x - 4·2 + 2x
= -4x - 8 + 2x
Combine like terms:
= (-4x + 2x) - 8
=
-2x - 8
✔ Answer: -2x - 8
---
9. 7(w - 5) + 3w
Distribute 7:
= 7·w - 7·5 + 3w
= 7w - 35 + 3w
Combine like terms:
= (7w + 3w) - 35
=
10w - 35
✔ Answer: 10w - 35
---
10. 5(x + 2) - 3(x - 4)
Distribute both 5 and -3:
= 5·x + 5·2 - 3·x + 3·4
= 5x + 10 - 3x + 12
Combine like terms:
= (5x - 3x) + (10 + 12)
=
2x + 22
✔ Answer: 2x + 22
---
11. -2(c - 2) + 4(c - 1)
Distribute -2 and 4:
= -2·c + 2·2 + 4·c - 4·1
= -2c + 4 + 4c - 4
Combine like terms:
= (-2c + 4c) + (4 - 4)
=
2c + 0
=
2c
✔ Answer: 2c
---
12. 3(b + 5) - (b - 2)
Distribute 3 and -1:
= 3·b + 3·5 - 1·b + 1·2
= 3b + 15 - b + 2
Combine like terms:
= (3b - b) + (15 + 2)
=
2b + 17
✔ Answer: 2b + 17
---
13. 4(x - 2) + 3(x + 9)
Distribute 4 and 3:
= 4·x - 4·2 + 3·x + 3·9
= 4x - 8 + 3x + 27
Combine like terms:
= (4x + 3x) + (-8 + 27)
=
7x + 19
✔ Answer: 7x + 19
---
##
✔ Final Answers Summary:
1.
8x + 32
2.
8a - 2
3.
-6x + 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 a worksheet version or to check your work! 😊
Parent Tip: Review the logic above to help your child master the concept of prealgebra review worksheet.
