Find the 4ᵗʰ term in the expansion of (x - 2y)¹²

Solution:

It is known that (r + 1)^th term, (Tᵣ ₊ ₁) in the binomial expansion of (a + b)ⁿ is given by Tᵣ ₊ ₁ = ⁿCᵣ aⁿ ⁻ ʳ bʳ.

Thus, the 4^th term in the expansion of (x - 2y)¹² is

T₄ = T₃ ₊ ₁

= ¹²C₃ (x)¹² ⁻ ³ (- 2y)³

= [12!/(3!9!)] (x)⁹ ( - 2)³ (y)³

= (12 × 11 × 10)/(3 × 2) ( - 8) x⁹y³

= - 1760 x⁹y³

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.2 Question 5

Find the 4ᵗʰ term in the expansion of (x - 2y)¹²

Summary:

Using the binomial theorem, the 4^th term in the expansion of (x - 2y)¹² is to be found. We have found that it is equal to - 1760 x⁹y³