Question

Factorise.

25a² − 4b² + 28bc − 49c²

Answer 1

25a² − 4b² + 28bc − 49c² 

= 25a² − (4b² − 28bc + 49c²)

= (5a)² − [(2b)² − 2 × 2b × 7c + (7c)²]

= (5a)² − [(2b − 7c)²]

[Using identity (a − b)² = a² − 2ab + b²]

= [5a + (2b − 7c)] [5a − (2b − 7c)]

[Using identity a² − b² = (a − b) (a + b)]

= (5a + 2b − 7c) (5a − 2b + 7c)