Question

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

a⁴ + a²b² + 25b⁴ 

Answer 1

Given expression: a⁴ + a²b² + 25b⁴ 

Now, using middle term factorisation method,

a⁴ + a²b² + 25b⁴ 

= a⁴ + 10a²b² – 9a²b² + 25b⁴

= a⁴ + 10a²b² + 25b⁴ – 9a²b²

= (a² + 5)² – (3ab)²  ...[∵ (a + b)² = a² + 2ab + b²]

= (a² + 5b² + 3ab)(a² + 5b² – 3ab)   ...[∵ a² – b² = (a + b) (a – b)]

The factorisation result is (a² + 5b² + 3ab) (a² + 5b² – 3ab).