Factorize the following expressions:
m³ + 8

The above equation can be simplified as

= (m)³ + (2)³
Both the given terms are perfect cubes, factor using the sum of cubes formula,

(a)³ + (b)³ = (a + b)(a² – ab + b²)
Here a = m and b = 2

⇒ (m)³ + (2)³ = (m + 2)((m)² – (m)(2) + (2)²)

= (m + 2)(m² – 2m + 4)
m³ + 8 = (m + 2)(m² – 2m + 4)