Question

Factorise:

a⁶ – 15625b⁶

Answer 1

Given expression is a⁶ – 15625b⁶

Applying the identity, we get,

⇒ (a³)² – [(5b)³]² = (a³ + [5b)³] [a³ – (5b)³]

We have

⇒ [a³ + (5b)³] = (a + 5b) [a² – 5ab + (5b)²]

And

⇒ [a³ – (5b)³] = (a – 5b) [a² + 5ab + (5b)²]

By grouping all these terms, we get,

⇒ (a + 5b) (a – 5b) (a² – 5ab + 25b²) (a² + 5ab + 25b²)

⇒ (a + 5b) (a – 5b) (a⁴ + 5a³b + 25a²b² – 5a³b – 25a²b² – 125ab³ + 25a²b² + 125ab³ + 625b⁴

⇒ (a + 5b) (a – 5b) (a⁴ + 625b⁴ + 25a²b²)

Hence, factors for the expression a⁶ – 15625b⁶ is (a + 5b) (a – 5b) (a⁴ + 625b⁴ + 25a²b²)