Question

Factorise: (a^4 - 8a^2b^2 + 16b^4) -81

Answer 1

Answer:(a² - 4b² - 9)(a² - 4b² + 9)

(a^4 - 8a²b² + 16b^4) - 81

= [(a²)² - 2.4a²b² + (4b²)²] - 9²

= (a² - 4b²)² - 9²

= (a² - 4b² - 9)(a² - 4b² + 9)

Step-by-step explanation:

Answer 2

Answer:

[(a - 2b)(a + 2b) + 9)][(a - 2b)(a + 2b) - 9]

This can be written as the difference of 2 squares:

(a^4 - 8a^2b^2 + 16b^4) -81

= (a^2 - 4b^2)^2 - 81

=[(a^2 - 4b^2) + 9] [(a^2 - 4b^2) - 9]

= [(a - 2b)(a + 2b) + 9)][(a - 2b)(a + 2b) - 9]