Question

Expand the following (1 – x + x²)⁴ 

Answer 1

Put 1 – x = y.

Then (1 – x + x²)⁴ = (y + x²)⁴

= ⁴C₀ y⁴(x²)⁰ + ⁴C₁ y³(x²)¹ + ⁴C₂ y²(x²)² + ⁴C₃ y(x²)³ + ⁴C₄ (x²)⁴

= y⁴ + 4y³ x² + 6y² x⁴ + 4y x⁶ + x⁸

= (1 – x)⁴ + 4x² (1 – x)³ + 6x⁴ (1 – x)² + 4x⁶ (1 – x) + x⁸

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