The coefficient of x^7 in the expansion of (1 - x - x^2 + x^3)^6 is

• Binomial Theorem

The coefficient of x⁷ in the expansion of (1 - x - x² + x³)⁶ is

1. 132
2. -132
3. 144
4. -144

Answer

(1 - x - x² + x³)⁶

= (1 - x)⁶(1 - x²)⁶

= (⁶C₀ - ⁶C₁ x + ... + ⁶C₆ x⁶)(⁶C₀ - ⁶C₁ x² + ... + ⁶C6 x¹²)

Now, coefficient of x⁷ is  = ⁶C₁ ⁶C₃ - ⁶C₃ ⁶C₂+ ⁶C₅ ⁶C₁

The correct option is D.