Maths · General term and middle term and simple applications
The total number of terms in the expansion of ^{50}+(x-y)^{50} \) is
The total number of terms in the expansion of \( (x+y)^{50}+(x-y)^{50} \) is
- A. 51
- B. 26
- C. 102 \)
- D. 25
Step-by-step solution
The expansion of (x+y)^50 has 51 terms, and (x-y)^50 also has 51 terms. When added, terms with odd powers of y cancel, leaving only terms with even powers of y. Since y's exponent ranges from 0 to 50, the even exponents are 0, 2, 4, ..., 50, giving (50/2)+1 = 26 terms.
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