x四次方-8x²y²-9y四次方

x四次方-8x²y²-9y四次方
x四次方-8x²y²-9y四次方

x四次方-8x²y²-9y四次方
x^4-8x²y²-9y^4
=(x²+y²)(x²-9y²)
=(x²+y²)(x+3y)(x-3y)

x四次方-8x²y²-9y四次方=(x^2-9y^2)(x^2+y^2)=(x+3)(x-3)(x^2+y^2)

稍等

原式=（x^2-9y^2）(x^2+y^2)
=(x+3y)(x-3y)(x^2+y^2)

设x^2=a,y^2=b
原式=a^2-8ab-9b^2
=(a-9b)(a+b)
再把x,y代入
=（x^2-9y^2)(x^2+y^2)
=（x+3y)(x-3y)(x^2+y^2)

x^4-8x²y²-9y^4=(x²)²-8x²y²-9(y²)²=(x²-9y²)(x²+y²)=(x²+y²)(x+3y)(x-3y)