# How do you use the binomial series to expand  (x+7)^17?

The binomial theorem states that

where

Hence

where

where ()! is the factorial function.

Hence we finally get

${\left(x + 7\right)}^{17} = {x}^{17} + 119 {x}^{16} + 6664 {x}^{15} + 233240 {x}^{14} + 5714380 {x}^{13} + 104001716 {x}^{12} + 1456024024 {x}^{11} + 16016264264 {x}^{10} + 140142312310 {x}^{9} + 980996186170 {x}^{8} + 5493578642552 {x}^{7} + 24471395771368 {x}^{6} + 85649885199788 {x}^{5} + 230595844768660 {x}^{4} + 461191689537320 {x}^{3} + 645668365352248 {x}^{2} + 564959819683217 x + 232630513987207$