Multiplying Binomials Practice Worksheet with 20 Problems and Example Solution

Let’s solve each problem step by step. We’re multiplying two binomials and writing the result in expanded form: ax² + bx + c.

We’ll use the FOIL method (First, Outer, Inner, Last) for each pair.

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1) (3v – 2)(2v + 5)

- First: 3v × 2v = 6v²
- Outer: 3v × 5 = 15v
- Inner: –2 × 2v = –4v
- Last: –2 × 5 = –10

Combine like terms:
6v² + (15v – 4v) – 10 = 6v² + 11v – 10

✔ Final Answer: 6v² + 11v – 10

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2) (2x – 3)(x + 4)

- First: 2x × x = 2x²
- Outer: 2x × 4 = 8x
- Inner: –3 × x = –3x
- Last: –3 × 4 = –12

Combine:
2x² + (8x – 3x) – 12 = 2x² + 5x – 12

✔ Final Answer: 2x² + 5x – 12

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3) (2m + 1)(5m + 5)

- First: 2m × 5m = 10m²
- Outer: 2m × 5 = 10m
- Inner: 1 × 5m = 5m
- Last: 1 × 5 = 5

Combine:
10m² + (10m + 5m) + 5 = 10m² + 15m + 5

✔ Final Answer: 10m² + 15m + 5

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4) (3a + 3)(5a – 1)

- First: 3a × 5a = 15a²
- Outer: 3a × (–1) = –3a
- Inner: 3 × 5a = 15a
- Last: 3 × (–1) = –3

Combine:
15a² + (–3a + 15a) – 3 = 15a² + 12a – 3

✔ Final Answer: 15a² + 12a – 3

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5) (4k + 3)(5k + 1)

- First: 4k × 5k = 20k²
- Outer: 4k × 1 = 4k
- Inner: 3 × 5k = 15k
- Last: 3 × 1 = 3

Combine:
20k² + (4k + 15k) + 3 = 20k² + 19k + 3

✔ Final Answer: 20k² + 19k + 3

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6) (3r + 3)(5r + 1)

- First: 3r × 5r = 15r²
- Outer: 3r × 1 = 3r
- Inner: 3 × 5r = 15r
- Last: 3 × 1 = 3

Combine:
15r² + (3r + 15r) + 3 = 15r² + 18r + 3

✔ Final Answer: 15r² + 18r + 3

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7) (5x – 4)(5x + 3)

- First: 5x × 5x = 25x²
- Outer: 5x × 3 = 15x
- Inner: –4 × 5x = –20x
- Last: –4 × 3 = –12

Combine:
25x² + (15x – 20x) – 12 = 25x² – 5x – 12

✔ Final Answer: 25x² – 5x – 12

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8) (3r + 4)(2r – 1)

- First: 3r × 2r = 6r²
- Outer: 3r × (–1) = –3r
- Inner: 4 × 2r = 8r
- Last: 4 × (–1) = –4

Combine:
6r² + (–3r + 8r) – 4 = 6r² + 5r – 4

✔ Final Answer: 6r² + 5r – 4

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9) (3n – 3)(3n + 5)

- First: 3n × 3n = 9n²
- Outer: 3n × 5 = 15n
- Inner: –3 × 3n = –9n
- Last: –3 × 5 = –15

Combine:
9n² + (15n – 9n) – 15 = 9n² + 6n – 15

✔ Final Answer: 9n² + 6n – 15

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10) (4x + 2)(x – 1)

- First: 4x × x = 4x²
- Outer: 4x × (–1) = –4x
- Inner: 2 × x = 2x
- Last: 2 × (–1) = –2

Combine:
4x² + (–4x + 2x) – 2 = 4x² – 2x – 2

✔ Final Answer: 4x² – 2x – 2

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11) (–2n – 6)(5n – 3)

- First: –2n × 5n = –10n²
- Outer: –2n × (–3) = 6n
- Inner: –6 × 5n = –30n
- Last: –6 × (–3) = 18

Combine:
–10n² + (6n – 30n) + 18 = –10n² – 24n + 18

✔ Final Answer: –10n² – 24n + 18

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12) (–7b + 7)(–6b – 6)

- First: –7b × –6b = 42b²
- Outer: –7b × –6 = 42b
- Inner: 7 × –6b = –42b
- Last: 7 × –6 = –42

Combine:
42b² + (42b – 42b) – 42 = 42b² + 0b – 42 = 42b² – 42

✔ Final Answer: 42b² – 42

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13) (4b – 8)(–8b – 8)

- First: 4b × –8b = –32b²
- Outer: 4b × –8 = –32b
- Inner: –8 × –8b = 64b
- Last: –8 × –8 = 64

Combine:
–32b² + (–32b + 64b) + 64 = –32b² + 32b + 64

✔ Final Answer: –32b² + 32b + 64

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14) (7a – 2)(–2a + 7)

- First: 7a × –2a = –14a²
- Outer: 7a × 7 = 49a
- Inner: –2 × –2a = 4a
- Last: –2 × 7 = –14

Combine:
–14a² + (49a + 4a) – 14 = –14a² + 53a – 14

✔ Final Answer: –14a² + 53a – 14

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15) (2b + 5)(–8b + 5)

- First: 2b × –8b = –16b²
- Outer: 2b × 5 = 10b
- Inner: 5 × –8b = –40b
- Last: 5 × 5 = 25

Combine:
–16b² + (10b – 40b) + 25 = –16b² – 30b + 25

✔ Final Answer: –16b² – 30b + 25

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16) (–a – 2)(–7a + 7)

- First: –a × –7a = 7a²
- Outer: –a × 7 = –7a
- Inner: –2 × –7a = 14a
- Last: –2 × 7 = –14

Combine:
7a² + (–7a + 14a) – 14 = 7a² + 7a – 14

✔ Final Answer: 7a² + 7a – 14

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17) (–8n – 4)(–4n + 3)

- First: –8n × –4n = 32n²
- Outer: –8n × 3 = –24n
- Inner: –4 × –4n = 16n
- Last: –4 × 3 = –12

Combine:
32n² + (–24n + 16n) – 12 = 32n² – 8n – 12

✔ Final Answer: 32n² – 8n – 12

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18) (–4n – 6)(4n – 8)

- First: –4n × 4n = –16n²
- Outer: –4n × –8 = 32n
- Inner: –6 × 4n = –24n
- Last: –6 × –8 = 48

Combine:
–16n² + (32n – 24n) + 48 = –16n² + 8n + 48

✔ Final Answer: –16n² + 8n + 48

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19) (5m – 1)(7m + 8)

- First: 5m × 7m = 35m²
- Outer: 5m × 8 = 40m
- Inner: –1 × 7m = –7m
- Last: –1 × 8 = –8

Combine:
35m² + (40m – 7m) – 8 = 35m² + 33m – 8

✔ Final Answer: 35m² + 33m – 8

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20) (7n – 2)(–n + 8)

- First: 7n × –n = –7n²
- Outer: 7n × 8 = 56n
- Inner: –2 × –n = 2n
- Last: –2 × 8 = –16

Combine:
–7n² + (56n + 2n) – 16 = –7n² + 58n – 16

✔ Final Answer: –7n² + 58n – 16

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## ✔ FINAL ANSWERS (All 20 Problems):

1) 6v² + 11v – 10
2) 2x² + 5x – 12
3) 10m² + 15m + 5
4) 15a² + 12a – 3
5) 20k² + 19k + 3
6) 15r² + 18r + 3
7) 25x² – 5x – 12
8) 6r² + 5r – 4
9) 9n² + 6n – 15
10) 4x² – 2x – 2
11) –10n² – 24n + 18
12) 42b² – 42
13) –32b² + 32b + 64
14) –14a² + 53a – 14
15) –16b² – 30b + 25
16) 7a² + 7a – 14
17) 32n² – 8n – 12
18) –16n² + 8n + 48
19) 35m² + 33m – 8
20) –7n² + 58n – 16