Question 2 Expand the expression (2/x - x/2)^5
Class X1 - Maths -Binomial Theorem Page 166
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(2/x-x/2)⁵
use the formula,
(x-y)ⁿ = ⁿC₀xⁿ -ⁿC₁xⁿ⁻¹.y +ⁿC₂xⁿ⁻².y².......(-1)ⁿ.ⁿCₙyⁿ
(2/x-x/2)⁵ = ⁵C₀(2/x)⁵ - ⁵C₁(2/x)⁴.(x/2) + ⁵C₂(2/x)³(x/2)² - ⁵C₃(2/x)²(x/2)³ + ⁵C₄(2/x)(x/2)⁴ - ⁵C₅(x/2)⁵
=⁵C₀32/x⁵ - ⁵C₁16/x⁴ₓ x/2 + ⁵C₂8/x³ ₓ x²/4 - ⁵C₃ 4/x² ₓ x³/8 + ⁵C₄2/x ₓ x⁴/16- ⁵C₅x⁵/32
=32/x⁵ - 5.16/x⁴ₓ x/2 + (5.4/2)8/x³ ₓ x²/4 - (5.4)/2 4/x² ₓ x³/8 + 5.2/x ₓ x⁴/16- x⁵/32
=32/x⁵ - 40/x³ + 20/x - 5x + 5x³/8 - x⁵/32
use the formula,
(x-y)ⁿ = ⁿC₀xⁿ -ⁿC₁xⁿ⁻¹.y +ⁿC₂xⁿ⁻².y².......(-1)ⁿ.ⁿCₙyⁿ
(2/x-x/2)⁵ = ⁵C₀(2/x)⁵ - ⁵C₁(2/x)⁴.(x/2) + ⁵C₂(2/x)³(x/2)² - ⁵C₃(2/x)²(x/2)³ + ⁵C₄(2/x)(x/2)⁴ - ⁵C₅(x/2)⁵
=⁵C₀32/x⁵ - ⁵C₁16/x⁴ₓ x/2 + ⁵C₂8/x³ ₓ x²/4 - ⁵C₃ 4/x² ₓ x³/8 + ⁵C₄2/x ₓ x⁴/16- ⁵C₅x⁵/32
=32/x⁵ - 5.16/x⁴ₓ x/2 + (5.4/2)8/x³ ₓ x²/4 - (5.4)/2 4/x² ₓ x³/8 + 5.2/x ₓ x⁴/16- x⁵/32
=32/x⁵ - 40/x³ + 20/x - 5x + 5x³/8 - x⁵/32
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