Note: This isn't really difficult; it's just tedious.
5(35(3^n−1)−29(2^n−1))−6(35(3^n−2)−29(2^n−2))5(35(3n−1)−29(2n−1))−6(35(3n−2)−29(2n−2))
=(5xx35)(3^n-1)-(5xx29)(2^n-1) + ((-6)xx35)(3^n-2)-(-6xx29)(2^n-2)=(5×35)(3n−1)−(5×29)(2n−1)+((−6)×35)(3n−2)−(−6×29)(2n−2)
=175(3^n-1)-145(2^n-1)+ (-210)(3^n-2) + 174(2^n-2)=175(3n−1)−145(2n−1)+(−210)(3n−2)+174(2n−2)
=175*color(red)(3^n) color(green)(- 175)-145*color(blue)(2^n)color(green)(+145)-210*color(red)(3^n)color(green)(+420)+174*color(blue)(2^n)color(green)(-348)=175⋅3n−175−145⋅2n+145−210⋅3n+420+174⋅2n−348
=(175-210)*color(red)(3^n)+(-145+420)*color(blue)(2^n)+(color(green)(-175+145+420-348))=(175−210)⋅3n+(−145+420)⋅2n+(−175+145+420−348)
=-35(3^n)+275(2^n)+42=−35(3n)+275(2n)+42
