Question

Find the 5th term in the expansion of (x – 2y)¹³.

Answer 1

General term is t_r+1 = nC_r x^n-r a^r

(x – 2y)¹³ = (x + (-2y))¹³

Here x is x, a is (-2y) and n = 13

5th term = t₅ = t₄₊₁ = 13C₄ x^13-4 (-2y)⁴

= 13C₄ x⁹ 2⁴ y⁴ 

`= (13xx12xx11xx10)/(4xx3xx2xx1)`× 2 × 2 × 2 × 2× x⁹y⁴

= 13 × 11 × 10 × 8x⁹y⁴

= 13 × 880x⁹y⁴

= 11440x⁹y⁴