Q88 / 180 · KCET 2019 · Mathematics
The number of terms in the expansion of \( \left(x^{2}+y^{2}\right)^{25}-\left(x^{2}-y^{2}\right)^{25} \) after simplification is
- Correct answerA\( 13 \)
- B\( 50 \)
- C\( 00 \)
- D\( 26 \)
Solution
(A)
\( (a+b)^{n}-(a-b)^{n} \) if \( \mathrm{n} \) is odd
On simplification we get \( \frac{n+1}{2} \) terms i.e., \( \frac{25+1}{2}=13 \) terms
\( (a+b)^{n}-(a-b)^{n} \) if \( \mathrm{n} \) is odd
On simplification we get \( \frac{n+1}{2} \) terms i.e., \( \frac{25+1}{2}=13 \) terms
Hence, the correct answer is option: 'A'.