Maths · Binomial theorem for a positive integral index
The number of dissimilar terms in the expansion of ^{20} \) is
The number of dissimilar terms in the expansion of \( \left(1-3 x+3 x^{2}-x^{3}\right)^{20} \) is
- A. 21
- B. 32
- C. 41
- D. 61
Step-by-step solution
The expression simplifies to (1-x)^60 using the identity (1-x)^3 = 1-3x+3x^2-x^3. The expansion of (1-x)^60 contains terms from x^0 to x^60, each with a distinct power, giving 61 dissimilar terms.