Expand (1 − x + x²)⁴ using binomial theorem.

By using binomial theorem,

(1 − x + x²)⁴ = [1 + (−x + x²)]⁴

Let y = −x + x², then (1 + y)⁴ = ⁴C₀ + ⁴C₁y + ⁴C₂y² + ⁴C₃y³ + ⁴C₄y⁴

= 1 + 4y + 6y² + 4y³ + y⁴

= 1 + 4(−x + x²) + 6(−x + x²)² + 4(−x + x²)³ + (−x + x²)⁴

= 1 − 4x + 4x² + 6(x² − 2x³ + x⁴) + 4(−x³ + 3x⁴ − 3x⁵ + x⁶) + (x⁴ − 4x⁵ + 6x⁶ − 4x⁷ + x⁸)

= 1 − 4x + 10x² − 8x³ + 19x⁴ − 16x⁵ + 10x⁶ − 4x⁷ + x⁸

Final Answer: (1 − x + x²)⁴ = 1 − 4x + 10x² − 8x³ + 19x⁴ − 16x⁵ + 10x⁶ − 4x⁷ + x⁸