Question

Find the 13th term of the binomial expansion of: (2x-4)^21 Please help :(

Answer 1

$T_r={n \choose r-1}a^{n-r+1}b^{r-1}\\ T_{13}={21 \choose 13-1}(2x)^{21-13+1}(-4)^{13-1}\\ T_{13}={21 \choose 12}(2x)^9(-4)^{12}\\ T_{13}=\frac{21!}{12!9!}\cdot512x^9\cdot16777216\\ T_{13}=293930\cdot8589934592x^9\\ T_{13}=2524839474626560x^9$