Factorise:

125x³ + 1

Given,

⇒ 125x³ + 1

⇒ (5x)³ + (1)³

By using the identity,

a³ + b³ = (a + b)(a² - ab + b²)

⇒ (5x + 1)[(5x)² - 5x × 1 + (1)²]

⇒ (5x + 1)(25x² - 5x + 1)

Hence, 125x³ + 1 = (5x + 1)(25x² - 5x + 1).