-Y*Y*Y+3Y*Y+9Y+5怎么转化成（Y+1）*（Y+1）(Y-5)

更新时间2019-04-05 18:07:08

这两个是不能转化的，因为前面那个y的三次方前是负号，后面这个y的三次方是正号

应该是：

-Y*Y*Y+3Y*Y+9Y+5

=-Y^3+3Y^2+9y+5

=-(Y^3-3Y^2-4Y)+(5Y+5)

=-Y(Y^2-3Y-4)+5(Y+1)

=-Y(Y+1)(Y-4)+5(Y+1)

=(Y+1)[-Y(Y-4)+5]

=(Y+1)(-Y^2+4Y+5)

=-(Y+1)(Y^2-4Y-5)

=-(Y+1)(Y+1)(Y-5)

前面应该有一个负号

-y³+3y²+9y+5≠(y+1)²(y-5)

证明：(y+1)²(y-5)

=(y²+2y+1)(y-5)

=y²(y-5)+2y(y-5)+(y-5)

=y³-5y²+2y²-10y+y-5

=y³-3y²-9y-5

原式＝－Ｙ²［ｙ＋１］＋［４Ｙ²＋９ｙ＋５］＝（Ｙ＋１）［－Ｙ²＋（４Ｙ＋５）］

＝－（ｙ＋１）（Ｙ＋１）（Ｙ－５）。

证明：原式=-Y*Y*Y+3Y*Y+9Y+5

               =-Y^3+3Y^2+9y+5

               =-(Y^3-3Y^2-4Y)+(5Y+5)

               =-Y(Y^2-3Y-4)+5(Y+1)

               =-Y(Y+1)(Y-4)+5(Y+1)

               =(Y+1)[-Y(Y-4)+5]

               =(Y+1)(-Y^2+4Y+5)

               =-(Y+1)(Y^2-4Y-5)

               =-(Y+1)(Y+1)(Y-5)。