Question
The coefficient of the highest power of x in the expansion of (x+ x^2-1 )^8+ (x- x^2-1 )^8
BITSAT
Mathematics
Binomial Theorem
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 64
- B. 128
- C. 256
- D. 512
Answer
C. 256
Step-by-step solution
Since (x+ x^2-1 )^8+ (x- x^2-1 )^8 array r =2 \ ^8 C_0 x^8+ ^8 C_2 x^6 (x^2-1 )+ ^8 C_4 x^4 (x^2-1 )^2 . \\ .+ ^8 C_6 x^2 (x^2-1 )^3+ ^8 C_8 x^0 (x^2-1 )^4 \ array So coefficient of highest power of x =2 \ ^8 C_0+ ^8 C_2+ ^8 C_4+ ^8 C_6+ ^8 C_8 \ =(1+1)^8+(1-1)^8=2^8=256
Related: Mathematics — Binomial Theorem · All PYQ Banks