Question

Factorise : \(x^8 - x^4 - 72\)

Answer 1

Let x⁴ = a. Then, \(x^8 - x^4 - 72\) = a² - a - 72

= a² - 9a + 8a - 72 = a(a - 9) + 8(a - 9)

= (a - 9)(a + 8) = (x⁴ - 9)(x⁴ + 8)

= ((x)² - 3²)(x⁴ + 8) = (x² + 3)(x² - 3)(x⁴ + 8).