Question

Question 4 Expand the expression (x/3 + 1/x)^5

Class X1 - Maths -Binomial Theorem Page 167

Answer 1

(x/3+ 1/x )⁵
use the formula,
(x + y)ⁿ = ⁿC₀xⁿ + ⁿC₁xⁿ⁻¹y + ⁿC₂xⁿ⁻²y²+ .......+ ⁿCₙyⁿ

(x/3+ 1/x )⁵ = ⁵C₀(x/3)⁵ + ⁵C₁(x/3)⁴(1/x) + ⁵C₂(x/3)³(1/x)² + ⁵C₃(x/3)²(1/x)³ + ⁵C₄(x/3)(1/x)⁴ + ⁵C₅(1/x)⁵

= ⁵C₀(x⁵/243) + ⁵C₁(x⁴/81 × 1/x) + ⁵C₂(x³/27 × 1/x²) + ⁵C₃(x²/9 × 1/x³) + ⁵C₄(x/3 × 1/x⁴) + ⁵C₅(1/x⁵)

= x⁵/243 + (5!/4!)x³/81 + (5!/3!×2!)x/27+ (5!/3!×2!)/9x +(5!/4!)/3x³ +(5!/5!) 1/x⁵

= x⁵/243 + 5x³/81 + 10x/27 + 10/9x + 5/3x³ + 1/x⁵