Question

若x＋y=-1则x的四次＋5x的三次y＋x的二次y＋8x的二次y的二次＋xy的二次＋5xy的三次＋y的四次的值等于?

Answer 1

x^4+5x^3y+x^2y+8x^2y^2+xy^2+5xy^3+y^4

=x^3(x+y)+4x^3y+x^2y+8x^2y^2+xy^2+y^3(x+y)+4xy^3

=-x^3-y^3+4xy(x^2+2xy+y^2)+xy(x+y)

=-(x+y)(x^2+y^2-xy)+4xy(x+y)^2-xy

=x^2+y^2-xy+4xy-xy

=x^2+y^2+2xy

=(x+y)^2

=1