Question

In the expansion of (1+ x² )⁸ , find the different between the coefficients of x⁶ and x⁴

Answer 1

Given expansion is (1 + x² )⁸

(1 + x² )⁸ = 1 + ⁸C₁ (1)^{8 – 1} (x² )¹ + ⁸C₂ (1)^{8 – 2} (x² ) ² + ⁸C₃ (1)8 – 3 (x²) 3 +⁸C₄ (1)^{8 – 4} (x² ) 4 + ⁸C₅ (1)^{8 – 5} (x² )⁵ + ⁸C₆ (1)⁸ – 6x² )⁶ +⁸C₇ (1)^{8 – 7} (x² )⁷ +⁸C⁸ (1)^{8 – 8} (x²)⁸ 

= 1 + 8x² + 28x⁴ + 56x⁶ + 70x⁸ + 56x⁰ + 28x² + 8x⁴ + x¹⁶

Coefficient of x⁶= 56 

Coefficient of x⁴ = 28 

∴ Different between the coefficients of x⁶ and x⁴

 = 56 – 28 = 28