x的四次方-xy的三次方-x的三次方y(tǒng)-3x的平方y(tǒng)+3xy的平方+y的四次方
=x的四次方-x的三次方y(tǒng)-3x的平方y(tǒng)+3xy的平方+y的四次方-xy的三次方
=x³(x-y)-3xy(x-y)-y³(x-y)
=(x³-3xy-y³)(x-y)
=[(x-y)(x²+xy+y²)-3xy](x-y)
因為y-x=1
所以x-y=-1
代入得
-(-x²-xy-y²-3xy)
=x²+4xy+y²
=(x+y)²+2xy
請核對題中是否有正負號的誤寫!

如果題目是
x的四次方-xy的三次方-x的三次方y(tǒng)+3x的平方y(tǒng)-3xy的平方+y的四次方
=x³(x-y)+3xy(x-y)-y³(x-y)
=(x³+3xy-y³)(x-y)
=[(x-y)(x²+xy+y²)+3xy](x-y)
=-(-x²-xy-y²+3xy)
=x²-2xy+y²
=(x-y)²
=1