Question

Factorise:

a³ – 216b³ – 7a + 42b

Answer 1

Given, a³ – 216b³ – 7a + 42b

a³ – 216b³ – 7a + 42b can also be written as {(a)³ – (6b)³ – 7(a – 6b)

Now, using the formula, 

x³ – y³ = (x – y) (x² + xy + y²)

⇒{(a – 6b) (a² + 6ab + 36b²)} – 7(a – 6b)

⇒ (a – 6b) {(a² + 6ab + 36b² – 7)}

Hence, the required is (a – 6b) {(a² + 6ab + 36b² – 7)}.