Question

Factorise: 

9(a − 2)² − 16(a + 2)²

Answer 1

9(a − 2)² − 16(a + 2)²

= 3(a − 2)² − [4(a + 2)]²

= [3(a − 2) + 4(a + 2)][3(a − 2) − 4(a + 2)]    ...[∵ a² − b² = (a + b)(a − b)]

= [3a − 6 + 4a + 8] [3a − 6 − 4a − 8]

= (7a + 2)(−a − 14)

= −(7a + 2)(a + 14)