x^5+3x^4y-5x^3y^2-15x^2y^3+4xy^4+12y^5 分解因式
问题描述：
x^5+3x^4y-5x^3y^2-15x^2y^3+4xy^4+12y^5 分解因式
答
x^5+3x^4y-5x^3y^2-15x^2y^3+4xy^4+12y^5 =x^5-5x^3y^2+4xy^4+12y^5-15x^2y^3+3x^4y =x(x^4-5x^2y^2+4y^4)+3y(x^4-5x^2y^2+4y^4) =(x+3y)(x^4-5x^2y^2+4y^4) =(x+3y)(x^2-4y^2)(x^2-y^2) =(x+3y)(x-2y)(x+2y)(x+y)(x...