Question

Factorise m⁴ – 256

Answer 1

m⁴ = (m²)² and 256 = (16)²

m⁴ – 256

= (m²)² – (16)²

= (m² – 16) (m² + 16)

Now,

(m² + 16) cannot be factorised further, but (m² – 16) is factorisable again as (a + b)(a - b) = a² - b²

m² – 16 = m² – 4² = (m – 4)(m + 4)

Therefore,

m⁴ – 256 = (m – 4)(m + 4)(m² + 16)