Question

Factorise:

49a² – 25b² + 60bc – 36c²

Answer 1

Given: 49a² – 25b² + 60bc – 36c²

49a² – 25b² + 60bc – 36c² can be written (7a)² – (25b² – 60bc + 36c²)

⇒ (7a)² – {(5b)² – 2 × 5b × 6c + (6c)²}

⇒ (7a)² – (5b – 6c)²

Now, applying the identity,

a² – b² = (a + b) (a – b)

⇒ (7a – 5b + 6c) (7a + 5b – 6c)

Hence, the required is (7a – 5b + 6c) (7a + 5b – 6c).