Question

(x4+y4)2-(2x2y2)2分解因式，求详细答案

Answer 1

(x4+y4)2-(2x2y2)2
=(x^4+y^4+2x²y²)(x^4+y^4-2x²y²)
=(x²+y²)²(x²-y²)²
=(x²+y²)²(x+y)²(x-y)²

追问

(x^4+y^4+2x²y²)(x^4+y^4-2x²y²)到(x²+y²)²(x²-y²)²是怎么回事

追答

x^4+y^4+2x²y²=(x²)²+2x²y²+(y²)²=(x²+y²)² 完全平方式

(x²-y²)²
=[(x+y)(x-y)]² (ab)²=a²b²
=(x+y)²(x-y)²