若m=x^3-3x^2y+2xy^2+3y^3,n=x^3-2x^2y+xy^2-5y^3,则2x^3-7x^y+5xy^2+14_数学解答

若m=x^3-3x^2y+2xy^2+3y^3,n=x^3-2x^2y+xy^2-5y^3,则2x^3-7x^y+5xy^2+14y^3的值是

人气：456 ℃　时间：2019-10-23 08:48:24

解答

m-n=8y^3+xy^2-x^2y
2x^3-7x^2y+5xy^2+14y^3
=(x^3-3x^2y+2xy^2+3y^3)+(x^3-2x^2y+xy^2-5y^3)-2x^2y+2xy^2+16y^3
=m+n+2(8y^3+xy^2-x^2y)
=m+n+2(m-n)
=3m-n