Question

因式分解，在线等！！！！

1. x^4+（四分之一）y^4
2. x^4-x^2y^2+16y^4

Answer 1

1. x^4+（四分之一）y^4
=x^4+1/4x^2y^2+1/4y^2-1/4x^2y^2
=(x^2+1/2y^2)^2-1/4x^2y^2
=(x^2+1/2y^2-1/2xy)(x^2+1/2y^2+1/2xy)

2. x^4-x^2y^2+16y^4
=x^4+16y^4+8x^2y^2-9x^2y^2
=(x^2+4y^2)^2-9x^2y^2
=(x^2+4y^2-3xy)(x^2+4y^2+3xy)
=(x-3y)(x-y)(x+y)(x+3y)

追问

x^4+（四分之一）y^4
=x^4+1/4x^2y^2+1/4y^2-1/4x^2y^2
=(x^2+1/2y^2)^2-1/4x^2y^2
=(x^2+1/2y^2-1/2xy)(x^2+1/2y^2+1/2xy)

=x^4+1/4x^2y^2+1/4y^2-1/4x^2y^2
这步错了吧！

追答

。。。
最近脑子容易犯迷糊，见谅啊
=x^4+x^2y^2+1/4y^2-1/4x^2y^2
=……
=(x^2+1/2y^2-xy)(x^2+1/2y^2+xy)

Answer 2

x^4+（四分之一）y^4
=x^4+x²y²+1/4y^4-x²y²
=(x²+1/2y²)²-x²y²
=(x²+xy+1/2y²)(x²-xy+1/2y²)

x^4-x^2y^2+16y^4
=x^4+8x²y²+16y^4-9x²y²
=(x²+4y²)²-9x²y²
=(x²-3xy+4y²)(x²+3xy+4y²)