Question

Factorise the following:

256x⁸ – y⁸

Answer 1

To factorise 256x⁸ – y⁸, we can use the difference of squares method.

First, recognize that:

256x⁸ – y⁸ = (16x⁴)² – y⁸

This is a difference of squares, which can be factorised using the formula:

A² – B² = (A – B) (A + B)

Here, A = 16x⁴ and B = y⁴

Applying the difference of squares:

(16x⁴ – y⁴)(16x⁴ + y⁴)

Next, notice that 16x⁴ – y⁴ is also a difference of squares and it can be further factorised.

Write it as 16x⁴ – y⁴ = (4x²)² – y⁴

Again, apply the difference of squares formula:

(4x² – y²) (4x² + y²)

Thus, the complete factorisation of 256x⁸ – y⁸ is (4x² – y²) (4x² + y²) (16x⁴ + y⁴)