分解因式 x(x-y)^5+xy(y-x)^4-x^3(x-y)3
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/24 08:08:25
分解因式 x(x-y)^5+xy(y-x)^4-x^3(x-y)3
分解因式 x(x-y)^5+xy(y-x)^4-x^3(x-y)3
分解因式 x(x-y)^5+xy(y-x)^4-x^3(x-y)3
=x(x-y)^3[(x-y)^2+y(x-y)-x^2]
=x(x-y)^3[(x-y)(x-y+y)-x^2]
=x(x-y)^3[(x-y)*x-x^2]
=x^2*(x-y)^3[(x-y)-x]
=-x^2*y*(x-y)^3
x(x-y)^5+xy(y-x)^4-x^3(x-y)3
=x(x-y)³【(x-y)²+y(x-y)-x²]
=x(x-y)³【x²-2xy+y²+xy-y²-x²]
=x(x-y)³(-xy)=-x²y(x-y)³谢谢，还有最后一道 -16(a+b)^4+81(...
全部展开
x(x-y)^5+xy(y-x)^4-x^3(x-y)3
=x(x-y)³【(x-y)²+y(x-y)-x²]
=x(x-y)³【x²-2xy+y²+xy-y²-x²]
=x(x-y)³(-xy)=-x²y(x-y)³
收起
x( x - y )^5 + xy( y - x )^4 - x"'( x - y )"'
= x( x - y )"'( x - y )" + x( x - y )"'( x - y )y - x"'( x - y )"'
= x( x - y )"'[ ( x - y )" + y( x - y ) - x" ]
= x( x - y )"'[ x" + y" - 2x...
全部展开
x( x - y )^5 + xy( y - x )^4 - x"'( x - y )"'
= x( x - y )"'( x - y )" + x( x - y )"'( x - y )y - x"'( x - y )"'
= x( x - y )"'[ ( x - y )" + y( x - y ) - x" ]
= x( x - y )"'[ x" + y" - 2xy + xy - y" - x" ]
= x( x - y )"'( -xy )
= - x"y( x - y )"'
- 16( a + b )^4 + 81( a - b )^4
= [ 9( a - b )" ]" - [ 4( a + b )" ]
= [ 3"( a - b )" - 2"( a + b )" ][ 9( a" - 2ab + b" ) + 4( a" + 2ab + b" ) ]
= [ ( 3a - 3b ) - ( 2a + 2b ) ][ ( 3a - 3b ) + ( 2a + 2b ) ]( 13a" + 13b" + 8ab - 18ab )
= ( a - 5b )( 5a - b )( 13a" - 10ab + 13b" )
收起