Take away:
(i) 65x2−45x3+56+32x from x33−52x2+35x+14
(ii) 5a22+3a32+a3−65 from 13a3−34a2−52
(iii) 74x3+35x2+12x+92 from 72−x3−x25
(iv) y33+73y2+12y+12 from 13−53y2
(v) 23ac−57ab+23bc from 32ab−74ac−56bc
(i) 65x2−45x3+56+32x from x33−52x2+35x+14=(x33−52x2+35x+14)−(65x2−45x3+56+32x)=x33−52x2+35x+14−65x2+45x3−56−32x=x33+45x3−52x2−65x2+35x−32x+14−56=(13+45)x3+(−52−65)x2+(35−32)x+(14−56)=5+1215x3+−25−1210x2+6−1510x+3−1012=1715x3−3710x2−910x−712
(ii) 5a22+3a32+a3−65 from 13a3−34a2−52=(13a3−34a2−52)−(5a22+3a32+a3−65)=13a3−34a2−52−52a2−32a3−a3+65=13a3−32a3−34a2−52a2−a3+65−52=(13−32)a3−(34+52)a2−(13)a+(65−52)=2−96a3−3+104a2−13a+12−2510=−76a3−134a2−13a−1310
(iii) 74x3+35x2+12x+92 from 72−x3−x25=(72−x3−x25)−(74x3+35x2+12x+92)=72−x3−x25−74x3−35x2−12x−92=−74x3−x25−35x2−x3−12x+72−92=−74x3−(15+35)x2−(13+12)x+7−92=−74x3−1+35x2−2+36x−22=−74x3−45x2−56x−1
(iv) y33+73y2+12y+12 from 13−53y2=(13−53y2)−(y33+73y2+12y+12)=13−53y2−y33−73y2−12y−12=−y33−(53+73)y2−12y−12+13=−y33−5+73y2−12y−3−26=−y33−123y2−12y−16=−13y3−4y2−12y−16
(v) 23ac−57ab+23bc from 32ab−74ac−56bc=(32ab−74ac−56bc)−(23ac−57ab+23bc)=32ab−74ac−56bc−23ac+57ab−23bc=32ab+57ab−56bc−23bc−74ac−23ac=(32+57)ab−(56+23)bc−(74+23)ac=21+1014ab−5+46bc−21+812ac=3114ab−96bc−2912ac=3114ab−32bc−2912ac