# 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: - Mathematics and Statistics

MCQ

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:

• 50

• 51

• 100

• 202

#### Solution

51

Explanation;

(x + y)100 = x100 + 100C1 x99 y + 100C2 x98 y2 + ... + y100

(x – y)100 = x100100C1 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")

Concept: General Term in Expansion of (a + b)n
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Miscellaneous Exercise 4 | Q I. (1) | Page 85