Question

Factorise the following:

x⁴ + 4

Answer 1

Given expression: x⁴ + 4

Step-wise calculation:

1. Start by recognizing x⁴ + 4 as x⁴ + 4 × 1⁴.

2. Rewrite the expression by adding and subtracting the same term:

x⁴ + 4 = (x⁴ + 4x² + 4) – 4x²

x⁴ + 4 = (x² + 2)² – (2x)²

3. This shows it’s a difference of squares: 

(x² + 2)² – (2x)² = (x² + 2 + 2x)(x² + 2 – 2x)

4. Simplify the terms inside the brackets:

(x² + 2x + 2)(x² – 2x + 2)