当X-y=1时,求代数式x 四次方-xy³-x³y-3x²y+3xy²+y四次方

当X-y=1时,求代数式x 四次方-xy³-x³y-3x²y+3xy²+y四次方
当X-y=1时,求代数式x 四次方-xy³-x³y-3x²y+3xy²+y四次方

当X-y=1时,求代数式x 四次方-xy³-x³y-3x²y+3xy²+y四次方
(x-y)^3=x³--3x²y+3xy²-y³
得 -3x²y+3xy=²(x-y)^3-(x³-y³)
原式=x(x³-y³)+(x-y)^3-(x³-y³)+y(y³-x³)
=(x³-y³)(x-y-1)+(x-y)^3
X-y=1 所以 X-y-1 =0
原式=0+1
=1

x ^4-xy³-x³y-3x²y+3xy²+y^4=x(x³-y³)-y(x³-y³)-3xy(x-y)
=(x-y)(x³-y³)-3xy(x-y) ( 因为x-y=1)
=(x³-y³)-3xy ...

全部展开

x ^4-xy³-x³y-3x²y+3xy²+y^4=x(x³-y³)-y(x³-y³)-3xy(x-y)
=(x-y)(x³-y³)-3xy(x-y) ( 因为x-y=1)
=(x³-y³)-3xy (立方差公式）
=(x-y)(x²+xy+y²)-3xy
= x²+xy+y²-3xy
=x²-2xy+y²
= (x-y)²
=1

收起

x³-y³-3xy