## Pages

### Solved Example 1

Factor x^3 - 8

### Solution

Rewrite 8 as 2^3,
x^3 - 2^3
Comparing with a^3 - b^3, we get
a = x and b = 2
Applying the formula of difference of cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2), we get
(x - 2)(x^2 + x*2 + 2^2)
Simplifying,
(x - 2)(x^2 + 2x + 4)

### Solved Example 2

Factor 8a^3 - b^3

### Solution

Rewrite 8 as 2^3,
(2a)^3 - b^3
Comparing with a^3 - b^3, we get,
a = 2a and b = b
Applying the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2), we get
(2a - b)((2a)^2 + (2a)(b) + b^2)
Simplifying,
(2a - b)(4a^2 + 2ab + b^2)

### Solved Example 3

Factor 1 - x^3

### Solution

Rewrite 1 as 1^3 (because 1^3 = 1 * 1 * 1 = 1).
1^3 - x^3
Comparing with a^3 - b^3, we get
a = 1 and b = x
Applying the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2), we get
(1 - x)(1^2 + 1*x + x^2)
Simplifying,
(1 - x)(1 + x + x^2)