Combining Like Terms and Distributive Property Worksheets with ... - Free Printable

Let's solve each expression step by step using the distributive property and then combine like terms to simplify.

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🔹 Distributive Property:

$$ a(b + c) = ab + ac $$

We'll distribute first, then combine like terms (terms with the same variable and exponent).

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1. $ 6x - 2(x + 4) $

Step 1: Distribute $-2$ to both $x$ and $4$:
$$
6x - 2x - 8
$$

Step 2: Combine like terms:
$$
(6x - 2x) - 8 = 4x - 8
$$

✔ Answer: $ \boxed{4x - 8} $

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2. $ -9 + 2(1 - 3s) $

Step 1: Distribute $2$:
$$
-9 + 2(1) - 2(3s) = -9 + 2 - 6s
$$

Step 2: Combine constants:
$$
(-9 + 2) - 6s = -7 - 6s
$$

✔ Answer: $ \boxed{-7 - 6s} $

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3. $ 9(-6a + 3) - 4 $

Step 1: Distribute $9$:
$$
9(-6a) + 9(3) - 4 = -54a + 27 - 4
$$

Step 2: Combine constants:
$$
-54a + 23
$$

✔ Answer: $ \boxed{-54a + 23} $

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4. $ 3x + 3(1 + 8x) $

Step 1: Distribute $3$:
$$
3x + 3(1) + 3(8x) = 3x + 3 + 24x
$$

Step 2: Combine like terms:
$$
(3x + 24x) + 3 = 27x + 3
$$

✔ Answer: $ \boxed{27x + 3} $

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5. $ -(n + 2) - 2n $

Step 1: Distribute the negative sign (which is $-1$):
$$
-1(n) -1(2) - 2n = -n - 2 - 2n
$$

Step 2: Combine like terms:
$$
(-n - 2n) - 2 = -3n - 2
$$

✔ Answer: $ \boxed{-3n - 2} $

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6. $ (s - 3)7.2 + 3s $

Note: This is $7.2(s - 3)$, so distribute $7.2$:
$$
7.2s - 21.6 + 3s
$$

Step 2: Combine like terms:
$$
(7.2s + 3s) - 21.6 = 10.2s - 21.6
$$

✔ Answer: $ \boxed{10.2s - 21.6} $

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7. $ \frac{1}{2} + 3(2u + \frac{1}{2}) $

Step 1: Distribute $3$:
$$
\frac{1}{2} + 3(2u) + 3\left(\frac{1}{2}\right) = \frac{1}{2} + 6u + \frac{3}{2}
$$

Step 2: Combine constants:
$$
\frac{1}{2} + \frac{3}{2} = 2
$$

So:
$$
6u + 2
$$

✔ Answer: $ \boxed{6u + 2} $

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8. $ 2x + 3(x - 1) $

Step 1: Distribute $3$:
$$
2x + 3x - 3
$$

Step 2: Combine like terms:
$$
(2x + 3x) - 3 = 5x - 3
$$

✔ Answer: $ \boxed{5x - 3} $

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9. $ -9(1 - 9a) + 7(2 + 9a) $

Step 1: Distribute both:
$$
-9(1) + (-9)(-9a) + 7(2) + 7(9a) = -9 + 81a + 14 + 63a
$$

Step 2: Combine like terms:
- Constants: $-9 + 14 = 5$
- Variables: $81a + 63a = 144a$

$$
144a + 5
$$

✔ Answer: $ \boxed{144a + 5} $

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10. $ \frac{1}{2}(3x - 9) + 13x $

Step 1: Distribute $\frac{1}{2}$:
$$
\frac{1}{2}(3x) - \frac{1}{2}(9) + 13x = \frac{3}{2}x - \frac{9}{2} + 13x
$$

Step 2: Combine like terms:
Convert $13x$ to fraction: $ \frac{26}{2}x $

$$
\left(\frac{3}{2}x + \frac{26}{2}x\right) - \frac{9}{2} = \frac{29}{2}x - \frac{9}{2}
$$

✔ Answer: $ \boxed{\frac{29}{2}x - \frac{9}{2}} $

(Or as mixed number: $14\frac{1}{2}x - 4\frac{1}{2}$, but improper fractions are fine.)

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11. $ -(y + 3) + 8(1 - 6y) $

Step 1: Distribute the negative and the 8:
$$
-1(y) -1(3) + 8(1) - 8(6y) = -y - 3 + 8 - 48y
$$

Step 2: Combine like terms:
- Variables: $-y - 48y = -49y$
- Constants: $-3 + 8 = 5$

$$
-49y + 5
$$

✔ Answer: $ \boxed{-49y + 5} $

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12. $ -3(8x + 4) + \frac{1}{2}(6x - 24) $

Step 1: Distribute both:
- $-3(8x) = -24x$, $-3(4) = -12$
- $\frac{1}{2}(6x) = 3x$, $\frac{1}{2}(-24) = -12$

So:
$$
-24x - 12 + 3x - 12
$$

Step 2: Combine like terms:
- Variables: $-24x + 3x = -21x$
- Constants: $-12 - 12 = -24$

$$
-21x - 24
$$

✔ Answer: $ \boxed{-21x - 24} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $4x - 8$ |
| 2 | $-7 - 6s$ |
| 3 | $-54a + 23$ |
| 4 | $27x + 3$ |
| 5 | $-3n - 2$ |
| 6 | $10.2s - 21.6$ |
| 7 | $6u + 2$ |
| 8 | $5x - 3$ |
| 9 | $144a + 5$ |
| 10 | $\frac{29}{2}x - \frac{9}{2}$ |
| 11 | $-49y + 5$ |
| 12 | $-21x - 24$ |

Let me know if you'd like these written in a different format!