Упростить многочлен:
(y2+3y−2)(y−1)(3c+4)(2c2−c−1)
Решение:
(y2+3y−2)(y−1)(3c+4)(2c2−c−1)=
Раскрытие скобок:
(y3+y2(−1)+3y2−3y−2y+2)(3c+4)(2c2−c−1)=(y3+2y2−5y+2)(3c+4)(2c2−c−1)=
Раскрытие скобок:
(y33c+y34+6y2c+8y2−15yc−20y+6c+8)(2c2−c−1)=(3y3c+4y3+6y2c+8y2−15yc−20y+6c+8)(2c2−c−1)=
Раскрытие скобок:
6y3c3−3y3c2−3y3c+8y3c2−4y3c−4y3+12y2c3−6y2c2−6y2c+16y2c2−8y2c−8y2−30yc3+15yc2+15yc−40yc2+20yc+20y+12c3−6c2−6c+16c2−8c−8=6y3c3+5y3c2−7y3c−4y3+12y2c3+10y2c2−14y2c−8y2−30yc3−25yc2+35yc+20y+12c3+10c2−14c−8=6c3y3+5c2y3+12c3y2−7cy3+10c2y2−30c3y−14cy2−4y3−25c2y+12c3+35cy−8y2+10c2+20y−14c−8
Ответ: 6c3y3+5c2y3+12c3y2−7cy3+10c2y2−30c3y−14cy2−4y3−25c2y+12c3+35cy−8y2+10c2+20y−14c−8