Question

Find the term independent of x in the expansion of (2/x+x^2)^12​

Answer 1

Answer:

126720

Step-by-step explanation:

By the binomial expansion, term independent of x is

$\displaystyle\binom{12}{4}\bigl(x^2\bigr)^4\bigl(\tfrac{2}{x}\bigr)^8\\\\=\binom{12}{4}\times 2^8\\\\=\frac{12\times 11\times 10\times 9 \times 2^8}{4\times 3\times 2\times 1}\\\\=12\times 11\times 10\times 3\times 2^5\\\\=126720$