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