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Question
Select the correct answer from the given alternatives.
The total number of terms in the expression of (x + y)100 + (x − y)100 after simplification is:
Options
50
51
100
202
Solution
51
Explanation;
(x + y)100 = x100 + 100C1 x99 y + 100C2 x98 y2 + ... + y100
(x – y)100 = x100 – 100C1 x99 y + 100C2 x98 y2 + ... + y100
(x + y)100 + (x – y)100 = `underbrace(2[x^100 + ""^100"C"_2 x^98 y^2 + ... + y^100])_(51 "terms")`
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