We can use Pascal's triangle to solve this problem.
The triangle values for the exponent 5 are:
#color(red)(1)color(white)(.........)color(red)(5)color(white)(.........)color(red)(10)color(white)(.........)color(red)(10)color(white)(.........)color(red)(5)color(white)(.........)color(red)(1)#
Therefore #(color(blue)(3u) color(green)(- 1))^5# can be multiplied as:
#color(red)(1)(color(green)((-1))^0color(blue)((3u))^5) + color(red)(5)(color(green)((-1))^1color(blue)((3u))^4) + color(red)(10)(color(green)((-1))^2color(blue)((3u))^3) + color(red)(10)(color(green)((-1))^3color(blue)((3u))^2) + color(red)(5)(color(green)((-1))^4color(blue)((3u))^1) + color(red)(1)(color(green)((-1))^5color(blue)((3u))^0)#
#color(red)(1)(1 * 243u^5) + color(red)(5)(-1 * 81u^4) + color(red)(10)(1 * 27u^3) + color(red)(10)(-1 * 9u^2) + color(red)(5)(1 * 3u) + color(red)(1)(-1 * 1)#
#color(red)(1)(243u^5) + color(red)(5)(-81u^4) + color(red)(10)(27u^3) + color(red)(10)(-9u^2) + color(red)(5)(3u) + color(red)(1)(-1)#
#243u^5 - 405u^4 + 270u^3 - 90u^2 + 15u - 1#
