Sure! Let’s solve each problem step by step using
the Distributive Property, which states:
>
a(b + c) = ab + ac
This means you multiply the term outside the parentheses by
each term inside the parentheses, then combine like terms if needed.
---
1) 3(8x + 6)
Multiply 3 by both terms inside:
= 3 × 8x + 3 × 6
=
24x + 18
---
2) -6(8k + 9)
Multiply -6 by both terms:
= (-6) × 8k + (-6) × 9
=
-48k - 54
---
3) -3(7m + 2)
Multiply -3 by both terms:
= (-3) × 7m + (-3) × 2
=
-21m - 6
---
4) (-2)(2x + 1) - (2 + 3x)
First, distribute -2:
= (-2)(2x) + (-2)(1) - (2 + 3x)
= -4x - 2 - 2 - 3x
Now combine like terms:
(-4x - 3x) + (-2 - 2)
=
-7x - 4
---
5) (-1)(7 + 6x)
Multiply -1 by both terms:
= (-1)(7) + (-1)(6x)
=
-7 - 6x
*(You can also write it as -6x - 7 — same thing.)*
---
6) (-7)(8x + 1)
Multiply -7 by both terms:
= (-7)(8x) + (-7)(1)
=
-56x - 7
---
7) (-5)(2x - 1) + 4(x + 3)
Distribute both parts:
= (-5)(2x) + (-5)(-1) + 4(x) + 4(3)
= -10x + 5 + 4x + 12
Combine like terms:
(-10x + 4x) + (5 + 12)
=
-6x + 17
---
8) (1 - 9x)(-8)
You can think of this as -8 distributed to both terms in (1 - 9x):
= (-8)(1) + (-8)(-9x)
= -8 + 72x
=
72x - 8
---
9) (-12)(6x + 1)
Multiply -12 by both terms:
= (-12)(6x) + (-12)(1)
=
-72x - 12
---
10) (-5)(8x - 6)
Multiply -5 by both terms:
= (-5)(8x) + (-5)(-6)
=
-40x + 30
---
11) (-10)(2x + 20)
Multiply -10 by both terms:
= (-10)(2x) + (-10)(20)
=
-20x - 200
---
12) (-12)(x - 1)
Multiply -12 by both terms:
= (-12)(x) + (-12)(-1)
=
-12x + 12
---
13) 5(2x + 14)
Multiply 5 by both terms:
= 5 × 2x + 5 × 14
=
10x + 70
---
14) (-5)(8x + 1) + 4(x + 2)
Distribute both parts:
= (-5)(8x) + (-5)(1) + 4(x) + 4(2)
= -40x - 5 + 4x + 8
Combine like terms:
(-40x + 4x) + (-5 + 8)
=
-36x + 3
---
##
✔ Final Answers:
1)
24x + 18
2)
-48k - 54
3)
-21m - 6
4)
-7x - 4
5)
-7 - 6x (or
-6x - 7)
6)
-56x - 7
7)
-6x + 17
8)
72x - 8
9)
-72x - 12
10)
-40x + 30
11)
-20x - 200
12)
-12x + 12
13)
10x + 70
14)
-36x + 3
---
Let me know if you’d like a printable version or more practice problems! 😊
Parent Tip: Review the logic above to help your child master the concept of distributive property of algebra worksheet.
