Factoring perfect trinomial worksheet - Free Printable

Sure! Let’s solve this worksheet step by step. The topic is Factoring Perfect Square Trinomials.

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## 🔷 PART A: Complete the expression to make a perfect square trinomial

A perfect square trinomial has the form:

> (x + b)² = x² + 2bx + b²
> or
> (x - b)² = x² - 2bx + b²

So, for an expression like a² + na + ___, we complete the square by taking half of n, then squaring it.

✔ Formula:
Missing term = (n/2)²

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Let's solve each one:

#### 1) a² + 8a + ___
Half of 8 = 4 → 4² = 16

✔ Answer: 16

#### 2) a² − 10a + ___
Half of -10 = -5 → (-5)² = 25

✔ Answer: 25

#### 3) a² + 4a + ___
Half of 4 = 2 → 2² = 4

✔ Answer: 4

#### 4) a² − 24a + ___
Half of -24 = -12 → (-12)² = 144

✔ Answer: 144

#### 5) a² − 4a + ___
Half of -4 = -2 → (-2)² = 4

✔ Answer: 4

#### 6) a² + 24a + ___
Half of 24 = 12 → 12² = 144

✔ Answer: 144

#### 7) a² + 12a + ___
Half of 12 = 6 → 6² = 36

✔ Answer: 36

#### 8) a² − 12a + ___
Half of -12 = -6 → (-6)² = 36

✔ Answer: 36

#### 9) a² − 6a + ___
Half of -6 = -3 → (-3)² = 9

✔ Answer: 9

#### 10) a² + 10a + ___
Half of 10 = 5 → 5² = 25

✔ Answer: 25

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## ✔ PART A Answers:
1) 16
2) 25
3) 4
4) 144
5) 4
6) 144
7) 36
8) 36
9) 9
10) 25

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## 🔷 PART B: Match Column A with its factor in Column B

We need to factor each trinomial in Column A and match it to the correct squared binomial in Column B.

Recall:
- If it’s a² + 2ab + b², it factors to (a + b)²
- If it’s a² - 2ab + b², it factors to (a - b)²

Let’s go one by one.

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1. a² + 8a + 16

→ This is (a + 4)² because 4²=16 and 2×a×4=8a
✔ Match: (a + 4)²

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2. a² − 10a + 25

→ (a - 5)² because 5²=25 and 2×a×5=10a (with minus sign)
✔ Match: (a - 5)²

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3. 4a² − 4a + 1

→ First term: (2a)², last term: 1², middle: 2×2a×1=4a → but it’s -4a → so (2a - 1)²
✔ Match: (2a - 1)²

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4. 4a² − 12a + 9

→ (2a)² - 2×2a×3 + 3² → (2a - 3)²
✔ Match: (2a - 3)²

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5. 4a² + 4a + 1

→ (2a + 1)² → 2×2a×1 = 4a
✔ Match: (2a + 1)²

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6. 9a² + 24a + 16

→ (3a)² + 2×3a×4 + 4² → (3a + 4)²
✔ Match: (3a + 4)²

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7. a² + 12a + 36

→ (a + 6)² → 6²=36, 2×a×6=12a
✔ Match: (a + 6)²

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8. a² − 12a + 36

→ (a - 6)² → 6²=36, 2×a×6=12a (minus)
✔ Match: (a - 6)²

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9. a² − 8a + 16

→ (a - 4)² → 4²=16, 2×a×4=8a (minus)
✔ Match: (a - 4)²

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10. a² + 10a + 25

→ (a + 5)² → 5²=25, 2×a×5=10a
✔ Match: (a + 5)²

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## ✔ PART B Matching Answers:

| Column A | Column B |
|------------------------------|----------------|
| 1. a² + 8a + 16 | → (a + 4)² |
| 2. a² − 10a + 25 | → (a - 5)² |
| 3. 4a² − 4a + 1 | → (2a - 1)² |
| 4. 4a² − 12a + 9 | → (2a - 3)² |
| 5. 4a² + 4a + 1 | → (2a + 1)² |
| 6. 9a² + 24a + 16 | → (3a + 4)² |
| 7. a² + 12a + 36 | → (a + 6)² |
| 8. a² − 12a + 36 | → (a - 6)² |
| 9. a² − 8a + 16 | → (a - 4)² |
| 10. a² + 10a + 25 | → (a + 5)² |

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## 🎯 Final Summary:

✔ Part A Answers:
1) 16 2) 25 3) 4 4) 144 5) 4 6) 144 7) 36 8) 36 9) 9 10) 25

✔ Part B Matches:
1 ↔ (a+4)²
2 ↔ (a−5)²
3 ↔ (2a−1)²
4 ↔ (2a−3)²
5 ↔ (2a+1)²
6 ↔ (3a+4)²
7 ↔ (a+6)²
8 ↔ (a−6)²
9 ↔ (a−4)²
10 ↔ (a+5)²

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