Question

Write no. of terms in the expansion of (1-3x+3x2-x3)8

Answer 1

Given :  (1-3x+3x²-x³)⁸

To Find : Number of terms in the expansion

Solution:

(1-3x+3x²-x³)⁸

= (1³+3(1)²(-x) +3(1)(-x)²)+ (-x)³)⁸

a³ + 3a²b + 3ab²  + b³ = (a + b)³

a = 1 , b = -x

= (( 1 - x)³)⁸

= (1 - x)²⁴

= (x - 1)²⁴   as power is even

(x - a)ⁿ  has n +1 terms

Hence number of terms in the expansion = 25  

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