Difference of Two Squares - Minimally Different - Free Printable

Problem: Factorize the given expressions using the difference of two squares formula.

The difference of two squares formula is:
\[
a^2 - b^2 = (a - b)(a + b)
\]

We will apply this formula to each expression step by step.

---

#### 1. \( x^2 - 16 \)
- Here, \( x^2 \) is \( a^2 \) and \( 16 \) is \( b^2 \).
- We can write \( 16 \) as \( 4^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
x^2 - 16 = x^2 - 4^2 = (x - 4)(x + 4)
\]

Answer:
\[
\boxed{(x - 4)(x + 4)}
\]

---

#### 2. \( x^2 - 25 \)
- Here, \( x^2 \) is \( a^2 \) and \( 25 \) is \( b^2 \).
- We can write \( 25 \) as \( 5^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
x^2 - 25 = x^2 - 5^2 = (x - 5)(x + 5)
\]

Answer:
\[
\boxed{(x - 5)(x + 5)}
\]

---

#### 3. \( x^2 - 36 \)
- Here, \( x^2 \) is \( a^2 \) and \( 36 \) is \( b^2 \).
- We can write \( 36 \) as \( 6^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
x^2 - 36 = x^2 - 6^2 = (x - 6)(x + 6)
\]

Answer:
\[
\boxed{(x - 6)(x + 6)}
\]

---

#### 4. \( 36 - x^2 \)
- Here, \( 36 \) is \( a^2 \) and \( x^2 \) is \( b^2 \).
- We can write \( 36 \) as \( 6^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
36 - x^2 = 6^2 - x^2 = (6 - x)(6 + x)
\]

Answer:
\[
\boxed{(6 - x)(6 + x)}
\]

---

#### 5. \( 4 - x^2 \)
- Here, \( 4 \) is \( a^2 \) and \( x^2 \) is \( b^2 \).
- We can write \( 4 \) as \( 2^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
4 - x^2 = 2^2 - x^2 = (2 - x)(2 + x)
\]

Answer:
\[
\boxed{(2 - x)(2 + x)}
\]

---

#### 9. \( 300 - 27x^2 \)
- First, factor out the greatest common factor (GCF) from both terms:
\[
300 - 27x^2 = 3(100 - 9x^2)
\]
- Now, focus on \( 100 - 9x^2 \):
- Here, \( 100 \) is \( a^2 \) and \( 9x^2 \) is \( b^2 \).
- We can write \( 100 \) as \( 10^2 \) and \( 9x^2 \) as \( (3x)^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
100 - 9x^2 = 10^2 - (3x)^2 = (10 - 3x)(10 + 3x)
\]
- Substitute back:
\[
300 - 27x^2 = 3(10 - 3x)(10 + 3x)
\]

Answer:
\[
\boxed{3(10 - 3x)(10 + 3x)}
\]

---

#### 10. \( 300 - 12x^2 \)
- First, factor out the greatest common factor (GCF) from both terms:
\[
300 - 12x^2 = 12(25 - x^2)
\]
- Now, focus on \( 25 - x^2 \):
- Here, \( 25 \) is \( a^2 \) and \( x^2 \) is \( b^2 \).
- We can write \( 25 \) as \( 5^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
25 - x^2 = 5^2 - x^2 = (5 - x)(5 + x)
\]
- Substitute back:
\[
300 - 12x^2 = 12(5 - x)(5 + x)
\]

Answer:
\[
\boxed{12(5 - x)(5 + x)}
\]

---

#### 11. \( 12x^2 - 300 \)
- First, factor out the greatest common factor (GCF) from both terms:
\[
12x^2 - 300 = 12(x^2 - 25)
\]
- Now, focus on \( x^2 - 25 \):
- Here, \( x^2 \) is \( a^2 \) and \( 25 \) is \( b^2 \).
- We can write \( 25 \) as \( 5^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
x^2 - 25 = x^2 - 5^2 = (x - 5)(x + 5)
\]
- Substitute back:
\[
12x^2 - 300 = 12(x - 5)(x + 5)
\]

Answer:
\[
\boxed{12(x - 5)(x + 5)}
\]

---

#### 12. \( 12x^2 - 3y^2 \)
- First, factor out the greatest common factor (GCF) from both terms:
\[
12x^2 - 3y^2 = 3(4x^2 - y^2)
\]
- Now, focus on \( 4x^2 - y^2 \):
- Here, \( 4x^2 \) is \( a^2 \) and \( y^2 \) is \( b^2 \).
- We can write \( 4x^2 \) as \( (2x)^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
4x^2 - y^2 = (2x)^2 - y^2 = (2x - y)(2x + y)
\]
- Substitute back:
\[
12x^2 - 3y^2 = 3(2x - y)(2x + y)
\]

Answer:
\[
\boxed{3(2x - y)(2x + y)}
\]

---

#### 13. \( 3x^2 - 3y^2 \)
- First, factor out the greatest common factor (GCF) from both terms:
\[
3x^2 - 3y^2 = 3(x^2 - y^2)
\]
- Now, focus on \( x^2 - y^2 \):
- Here, \( x^2 \) is \( a^2 \) and \( y^2 \) is \( b^2 \).
- Using the formula \( a^2 - b^2 = (a - b)(a + b) \):
\[
x^2 - y^2 = (x - y)(x + y)
\]
- Substitute back:
\[
3x^2 - 3y^2 = 3(x - y)(x + y)
\]

Answer:
\[
\boxed{3(x - y)(x + y)}
\]

---

Final Answers:

1. \(\boxed{(x - 4)(x + 4)}\)
2. \(\boxed{(x - 5)(x + 5)}\)
3. \(\boxed{(x - 6)(x + 6)}\)
4. \(\boxed{(6 - x)(6 + x)}\)
5. \(\boxed{(2 - x)(2 + x)}\)
9. \(\boxed{3(10 - 3x)(10 + 3x)}\)
10. \(\boxed{12(5 - x)(5 + x)}\)
11. \(\boxed{12(x - 5)(x + 5)}\)
12. \(\boxed{3(2x - y)(2x + y)}\)
13. \(\boxed{3(x - y)(x + y)}\)