Question

Factorise the following:

x⁵ – 64x²

Answer 1

Given expression: x⁵ – 64x²

Step-wise calculation:

Step 1: Take out the common factor. 

Both terms share (x²) as a factor:

x⁵ – 64x² = x²(x³ – 64)

Step 2: Recognize the difference of cubes in the bracket:

x³ – 64 = x³ – 4³

Use the factorization formula for the difference of cubes:

a³ – b³ = (a – b)(a² + ab + b²)

Substitute a = x and b = 4:

x³ – 4³ = (x – 4)(x² + 4x + 16)