已知X+3Y=0,求X³+3X²Y-2X-6Y的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/16 05:49:15

已知X+3Y=0,求X³+3X²Y-2X-6Y的值
已知X+3Y=0,求X³+3X²Y-2X-6Y的值

已知X+3Y=0,求X³+3X²Y-2X-6Y的值
x+3y=0
x^3+3x^2y-2x-6y
=x^2(x+3y)-2(x+3y)
=0-0
=0

X³+3X²Y-2X-6Y
=(X+3Y)(x^2-2)
=0


分解因式:
X³+3X²Y-2X-6Y=X(X^2-2)+3Y(X^2-2)=(X+3Y)(X^2-2)
而X+3Y=0,
故:
X³+3X²Y-2X-6Y=0