This worksheet provides 20 practice problems for students to factorize algebraic expressions using the greatest common divisor.

Absolutely! Let's solve this worksheet step by step. The goal is to factor each expression using the distributive property, which means we're looking for the greatest common factor (GCF) of the terms and then “pulling it out” in front of parentheses.

The distributive property says:
a(b + c) = ab + ac
So factoring is the reverse:
ab + ac = a(b + c)

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Let’s go through each problem:

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1) `3a + 15`

- GCF of 3 and 15 is 3
- 3a ÷ 3 = a
- 15 ÷ 3 = 5
✔ Factored: `3(a + 5)`

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2) `2b + 30`

- GCF of 2 and 30 is 2
- 2b ÷ 2 = b
- 30 ÷ 2 = 15
✔ Factored: `2(b + 15)`

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3) `6c - 18`

- GCF of 6 and 18 is 6
- 6c ÷ 6 = c
- 18 ÷ 6 = 3 → but since it’s minus, keep the sign
✔ Factored: `6(c - 3)`

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4) `5d - 45`

- GCF of 5 and 45 is 5
- 5d ÷ 5 = d
- 45 ÷ 5 = 9
✔ Factored: `5(d - 9)`

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5) `30 - 3e`

- GCF of 30 and 3 is 3
- 30 ÷ 3 = 10
- 3e ÷ 3 = e → but note: the term is subtracted
✔ Factored: `3(10 - e)`

*(Note: You could also write `3(-e + 10)`, but standard form puts positive first.)*

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6) `28 - 7f`

- GCF of 28 and 7 is 7
- 28 ÷ 7 = 4
- 7f ÷ 7 = f
✔ Factored: `7(4 - f)`

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7) `12g + 20`

- GCF of 12 and 20 is 4
- 12g ÷ 4 = 3g
- 20 ÷ 4 = 5
✔ Factored: `4(3g + 5)`

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8) `14h - 21`

- GCF of 14 and 21 is 7
- 14h ÷ 7 = 2h
- 21 ÷ 7 = 3
✔ Factored: `7(2h - 3)`

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9) `15i + 24`

- GCF of 15 and 24 is 3
- 15i ÷ 3 = 5i
- 24 ÷ 3 = 8
✔ Factored: `3(5i + 8)`

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10) `32 - 12j`

- GCF of 32 and 12 is 4
- 32 ÷ 4 = 8
- 12j ÷ 4 = 3j
✔ Factored: `4(8 - 3j)`

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11) `14k - 10`

- GCF of 14 and 10 is 2
- 14k ÷ 2 = 7k
- 10 ÷ 2 = 5
✔ Factored: `2(7k - 5)`

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12) `16l + 10`

- GCF of 16 and 10 is 2
- 16l ÷ 2 = 8l
- 10 ÷ 2 = 5
✔ Factored: `2(8l + 5)`

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13) `5m + 15n`

- GCF of 5 and 15 is 5
- 5m ÷ 5 = m
- 15n ÷ 5 = 3n
✔ Factored: `5(m + 3n)`

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14) `10p - 12q`

- GCF of 10 and 12 is 2
- 10p ÷ 2 = 5p
- 12q ÷ 2 = 6q
✔ Factored: `2(5p - 6q)`

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15) `20r + 16s`

- GCF of 20 and 16 is 4
- 20r ÷ 4 = 5r
- 16s ÷ 4 = 4s
✔ Factored: `4(5r + 4s)`

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16) `24 - 18t`

- GCF of 24 and 18 is 6
- 24 ÷ 6 = 4
- 18t ÷ 6 = 3t
✔ Factored: `6(4 - 3t)`

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17) `12u + 15v`

- GCF of 12 and 15 is 3
- 12u ÷ 3 = 4u
- 15v ÷ 3 = 5v
✔ Factored: `3(4u + 5v)`

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18) `32w + 18`

- GCF of 32 and 18 is 2
- 32w ÷ 2 = 16w
- 18 ÷ 2 = 9
✔ Factored: `2(16w + 9)`

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19) `40 - 28x`

- GCF of 40 and 28 is 4
- 40 ÷ 4 = 10
- 28x ÷ 4 = 7x
✔ Factored: `4(10 - 7x)`

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20) `18y + 36z`

- GCF of 18 and 36 is 18
- 18y ÷ 18 = y
- 36z ÷ 18 = 2z
✔ Factored: `18(y + 2z)`

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## ✔ Final Answer Key:

| Expression | Factored Expression |
|------------------|----------------------|
| 1) 3a + 15 | 3(a + 5) |
| 2) 2b + 30 | 2(b + 15) |
| 3) 6c - 18 | 6(c - 3) |
| 4) 5d - 45 | 5(d - 9) |
| 5) 30 - 3e | 3(10 - e) |
| 6) 28 - 7f | 7(4 - f) |
| 7) 12g + 20 | 4(3g + 5) |
| 8) 14h - 21 | 7(2h - 3) |
| 9) 15i + 24 | 3(5i + 8) |
| 10) 32 - 12j | 4(8 - 3j) |
| 11) 14k - 10 | 2(7k - 5) |
| 12) 16l + 10 | 2(8l + 5) |
| 13) 5m + 15n | 5(m + 3n) |
| 14) 10p - 12q | 2(5p - 6q) |
| 15) 20r + 16s | 4(5r + 4s) |
| 16) 24 - 18t | 6(4 - 3t) |
| 17) 12u + 15v | 3(4u + 5v) |
| 18) 32w + 18 | 2(16w + 9) |
| 19) 40 - 28x | 4(10 - 7x) |
| 20) 18y + 36z | 18(y + 2z) |

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## 💡 Tip:
Always check your answer by distributing the factor back in — you should get the original expression!

Example: For #1, `3(a + 5) = 3a + 15` ✔️

You’ve got this! Happy factoring! 🧮