因式分解：x^4+2x^2y^2+9y^4
问题描述：
因式分解：x^4+2x^2y^2+9y^4
答
x^4-2x^3y+4/3x^2y^2-8/27xy^3
=x[x^3-2x^2y+4/3xy^2-(2/3y)^3]
=x{[x^3-(2/3y)^3]-2xy(x-2/3y)}
=x[(x-2/3y)(x^2+2/3xy+4/9y^2)-2xy(x-2/3y)]
=x(x-2/3y)(x^2+2/3xy+4/9y^2-2xy)
=x(x-2/3y)(x^2-4/3xy+4/9y^2)
=x(x-2/3y)(x-2/3y)^2
=x(x-2/3y)^3
答
x^4+2x^2y^2+9y^4
=x^4+6x^2y^2+9y^4-4x^2y^2
=(x^2+3y^2)^2-(2xy)^2
=(x^2+2xy+3y^2)(x^2-2xy+3y^2)