## Pages

### Solved Example 1

Factor x^2 - 4

### Solution

Rewrite 4 as 2^2
x^2 – 4 = x^2 – 2^2
Comparing with a^2 – b^2, we get a = x and b = 2. Applying the formula a^2 – b^2 = (a + b)(a – b), we get
x^2 – 2^2 = (x + 2)(x – 2)

### Solved Example 2

Factor x^4 – 81

### Solution

Rewrite x^4 as (x^2)^2 and 81 as 9^2. Thus, we get
x^4 – 81 = (x^2)^2 – 9^2
Comparing with a^2 – b^2, we get a = x^2 and b = 9. Applying the formula a^2 – b^2 = (a + b)(a – b), we get
(x^2)^2 – 9^2 = (x^2 + 9)(x^2 – 9)
Rewrite 9 as 3^2
(x^2 + 9)(x^2 – 9) = (x^2 + 9)(x^2 – 3^2)
Again applying the formula a^2 – b^2 = (a + b)(a – b), we get
(x^2 + 9)(x^2 – 3^2) = (x^2 + 9)(x + 3)(x – 3)

### Solved Example 3

Factor 2x^2 – 72

### Solution

Factor out 2 from the given expression,
= 2(x^2 – 36)
Rewrite 36 as 6^2.
 = 2(x^2 – 6^2)
Applying the formula a^2 – b^2 = (a + b)(a – b), we get
= 2(x + 6)(x – 6)

### Solved Example 4

Factor a^2 – b^4

### Solution

Rewrite b^4 as (b^2)^2  to get
a^2 – (b^2)^2
Applying the formula a^2 – b^2 = (a + b)(a – b), we get
(a + b^2)(a – b^2)

### Solved Example 5

Factor 25x^2 – 36y^2

### Solution

Rewrite 25 as 5^2 and 36 as 6^2.
(5x)^2 – (6y)^2
Applying the formula a^2 – b^2 = (a + b)(a – b), we get
(5x + 6y)(5x – 6y)

### Solved Example 6

Factor 32x^3 – 50x

### Solution

Factor out 2x from the given expression,
= 2x(16x^2 – 25)
Rewrite 16 as 4^2 and 25 as 5^2
= 2x((4x)^2 – 5^2)
Applying the formula a^2 – b^2 = (a + b)(a – b),
= 2x(4x + 5)(4x – 5)