Question

化简求值:2x^3·y^2[xy(1-x)-2x(y-1/2)]2x^4·y^3(x+1)，其中x^2·y=-1/4

Answer 1

答：楼主，你的题目有问题啊.....请检查后追问，谢谢

2x^3·y^2[xy(1-x)-2x(y-1/2)]2x^4·y^3(x+1)，其中x^2·y=-1/4
原式
=2x³y²*[xy(1-x)-2x(y-1/2)]*(2x^4)*y³(x+1)
=2(x²y)(xy)*[xy-x²y-2xy+x]*2(x²y)²(yx+y)
=4*(-1/4)*(xy)(-x²y-xy+x)*(-1/4)²*(yx+y)
=(-1/16)*(x²y)(-xy-y+1)*(yx+y)
=(-1/16)*(-1/4)*(-x²y²-xy²-xy²-y²+xy+y)
=(1/64)*(-y/4-2xy²-y²+xy+y)
.............

追问

哦，化简:2x^3y^2[xy(1-x)-2x(y-1/2)]+2x^4y^3(x+1)，其中x^2y=-1/4

追答

答：
2x^3y^2[xy(1-x)-2x(y-1/2)]+2x^4y^3(x+1)，其中x^2y=-1/4

=2*(x²y)*(xy)*(xy-x²y-2xy+x)+2(x²y)²(xy+y)
=2*(-1/4)*(xy)*(-xy+1/4+x)+2*(-1/4)²(xy+y)
=-(1/2)*(-x²yy+xy/4+x²y)+(1/8)(xy+y)
=-(1/2)*(y/4+xy/4-1/4-xy/4-y/4)
=-(1/2)*(-1/4)
=1/8