Distributive Property and Combining Like Terms worksheet | Live ... - Free Printable

Let's solve each problem step by step and match the answers to the corresponding letters. Then we'll use those letters to decode the riddle: "Why do bees have sticky hair?"

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Step 1: Solve Each Problem

#### 1. $ 5(2x + 3) $
Distribute:
$$
5 \cdot 2x = 10x,\quad 5 \cdot 3 = 15
\Rightarrow 10x + 15
$$
Match: O. 10x + 15

---

#### 2. $ 8(3m + 4) $
Distribute:
$$
8 \cdot 3m = 24m,\quad 8 \cdot 4 = 32
\Rightarrow 24m + 32
$$
Match: E. 24m + 32

---

#### 3. $ 4(3 - 2y) $
Distribute:
$$
4 \cdot 3 = 12,\quad 4 \cdot (-2y) = -8y
\Rightarrow 12 - 8y
$$
Match: B. 12 - 8y

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#### 4. $ (8 + 3n)(6) $
Distribute:
$$
6 \cdot 8 = 48,\quad 6 \cdot 3n = 18n
\Rightarrow 48 + 18n
$$
Match: A. 48 + 18n

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#### 5. $ 6(2x - 3) $
Distribute:
$$
6 \cdot 2x = 12x,\quad 6 \cdot (-3) = -18
\Rightarrow 12x - 18
$$
Match: Y. 12x - 18

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#### 6. $ 9(2x + 6y) $
Distribute:
$$
9 \cdot 2x = 18x,\quad 9 \cdot 6y = 54y
\Rightarrow 18x + 54y
$$
Match: E. 18x + 54y

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#### 7. $ 7(x + 2y) $
Distribute:
$$
7x + 14y
$$
Match: T. 7x + 14y

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#### 8. $ 8(4x - 3y) $
Distribute:
$$
32x - 24y
$$
Match: O. 32x - 24y

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#### 9. $ 2(3x + 4) + 6 $
Distribute:
$$
6x + 8 + 6 = 6x + 14
$$
Match: E. 6x + 14

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#### 10. $ 3(x + 4) + 2x $
Distribute:
$$
3x + 12 + 2x = 5x + 12
$$
Match: S. 5x + 12

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#### 11. $ 4(2x + 3y) + 7x $
Distribute:
$$
8x + 12y + 7x = 15x + 12y
$$
Match: H. 15x + 12y

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#### 12. $ 8(3 - 2f) + 3 $
Distribute:
$$
24 - 16f + 3 = 27 - 16f
$$
Match: N. 27 - 16f

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#### 13. $ (9n + 6)(4) + 3n $
Distribute:
$$
36n + 24 + 3n = 39n + 24
$$
Match: V. 39n + 24

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#### 14. $ 5m + 7(2 + 8m) $
Distribute:
$$
5m + 14 + 56m = 61m + 14
\Rightarrow 14 + 61m
$$
Match: H. 14 + 61m

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#### 15. $ 6(x + y) + x $
Distribute:
$$
6x + 6y + x = 7x + 6y
$$
Match: C. 7x + 6y

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#### 16. $ 3 + 9(2n + 1) + 4n $
Distribute:
$$
3 + 18n + 9 + 4n = 22n + 12
$$
Match: H. 22n + 12

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#### 17. $ 2(5x + 2y) + 3(2y + x) $
Distribute:
$$
10x + 4y + 6y + 3x = 13x + 10y
$$
Match: M. 13x + 10y

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#### 18. $ 2(7 - 3x) + 6(3 + 2y) + 3y + 2 $
Distribute:
$$
14 - 6x + 18 + 12y + 3y + 2 = -6x + 15y + 34
\Rightarrow 34 - 6x + 15y
$$
Match: Y. 34 - 6x + 15y

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Step 2: Match Answers to Letters

Now, list the answers for each problem:

| Problem | Answer | Letter |
|--------|--------|--------|
| 1 | 10x + 15 | O |
| 2 | 24m + 32 | E |
| 3 | 12 - 8y | B |
| 4 | 48 + 18n | A |
| 5 | 12x - 18 | Y |
| 6 | 18x + 54y | E |
| 7 | 7x + 14y | T |
| 8 | 32x - 24y | O |
| 9 | 6x + 14 | E |
| 10 | 5x + 12 | S |
| 11 | 15x + 12y | H |
| 12 | 27 - 16f | N |
| 13 | 39n + 24 | V |
| 14 | 14 + 61m | H |
| 15 | 7x + 6y | C |
| 16 | 22n + 12 | H |
| 17 | 13x + 10y | M |
| 18 | 34 - 6x + 15y | Y |

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Step 3: Fill in the Box

The box at the bottom has numbers:

```
[7] [14] [2] [5] [11] [4] [13] [9] [16] [1] [12] [6] [18] [15] [8] [17] [3] [10]
```

We now plug in the letters from the answers of those problems:

| Number | Problem | Letter |
|--------|--------|--------|
| 7 | 7x + 14y → T | T |
| 14 | 14 + 61m → H | H |
| 2 | 24m + 32 → E | E |
| 5 | 12x - 18 → Y | Y |
| 11 | 15x + 12y → H | H |
| 4 | 48 + 18n → A | A |
| 13 | 39n + 24 → V | V |
| 9 | 6x + 14 → E | E |
| 16 | 22n + 12 → H | H |
| 1 | 10x + 15 → O | O |
| 12 | 27 - 16f → N | N |
| 6 | 18x + 54y → E | E |
| 18 | 34 - 6x + 15y → Y | Y |
| 15 | 7x + 6y → C | C |
| 8 | 32x - 24y → O | O |
| 17 | 13x + 10y → M | M |
| 3 | 12 - 8y → B | B |
| 10 | 5x + 12 → S | S |

So the sequence is:

T H E Y H A V E H O N E Y C O M B S

Wait — let's write it out clearly:

> 7 → T
> 14 → H
> 2 → E
> 5 → Y
> 11 → H
> 4 → A
> 13 → V
> 9 → E
> 16 → H
> 1 → O
> 12 → N
> 6 → E
> 18 → Y
> 15 → C
> 8 → O
> 17 → M
> 3 → B
> 10 → S

So the full phrase is:

THEY HAVE HONEY COMBS

But that doesn't make sense.

Wait — let's double-check the order:

The box says:

```
[7] [14] [2] [5] [11] [4] [13] [9] [16] [1] [12] [6] [18] [15] [8] [17] [3] [10]
```

So the letters are:

1. 7 → T
2. 14 → H
3. 2 → E
4. 5 → Y
5. 11 → H
6. 4 → A
7. 13 → V
8. 9 → E
9. 16 → H
10. 1 → O
11. 12 → N
12. 6 → E
13. 18 → Y
14. 15 → C
15. 8 → O
16. 17 → M
17. 3 → B
18. 10 → S

So putting them together:

T H E Y H A V E H O N E Y C O M B S

That’s THEY HAVE HONEYCOMBS

Ah! The joke is a pun: "Why do bees have sticky hair?"

Because they have honeycombs — but “honey combs” sounds like “honeycomb” — and their hair gets sticky with honey!

But wait — "honey combs" is plural, but the word is usually "honeycomb" (singular). But here it's a play on words: "They have honey combs" → "they have honeycomb", but written as if it's multiple.

But actually, "honeycombs" is correct.

So the answer is:

> They have honeycombs.

But the riddle is: Why do bees have sticky hair?

Answer: Because they have honeycombs — meaning they collect honey, which makes their hair sticky.

It's a pun: "They have honey combs" sounds like "They have honeycomb", but also plays on "sticky" because honey is sticky.

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✔ Final Answer:

They have honeycombs.

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🔤 Decoded Phrase:

From the box:

T H E Y H A V E H O N E Y C O M B S

→ THEY HAVE HONEYCOMBS

So the answer to the riddle is:

> Because they have honeycombs!

This is a pun on "honeycombs" sounding like "honey comb" (as in "sticky") — but more likely, it's just a clever joke.

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✔ Final Answer to Riddle:

Because they have honeycombs. 😊

(And yes, that's why their hair is sticky — covered in honey!)