Question

Factorise by splitting the middle term to get two perfect squares.

a⁴ – 7a²b² + b⁴

Answer 1

Given expression: a⁴ – 7a²b² + b⁴ 

Now, using middle term factorisation method,

a⁴ – 7a²b² + b⁴ 

= a⁴ + 2a²b² – 9a²b² + b⁴

= a⁴ + 2a²b² + b⁴ – 9a²b²

=  (a² + b²)² – (3ab)²     ...[∵ (a + b)² = a² + 2ab + b²]

= (a² + b² + 3ab) (a² + b² – 3ab)    ...[∵ a² – b² = (a + b) (a – b)]

The factorisation result is (a² + b² + 3ab) (a² + b² – 3ab).