3(x^2+y^2)^2-12x^2y^2因式分解

分类: 作业答案 • 2022-04-10 12:29:56

问题描述：

答

3(x^2+y^2)^2-12x^2y^2=3((x^2+y^2)^2-4x^2y^2)=3(x^2+y^2-2xy)(x^2+y^2+2xy)=3(x-y)^2(x+y)^2

答

3(x^2+y^2)^2-12x^2y^2
=3[(x²+y²)²-4x²y²]
=3[(x^4+2x²y²+y^4-4x²y²]
=3(x²-y²)²
=3(x-y)²(x+y)²

答

3(x^2+y^2)^2-12x^2y^2=3[(x^2+y^2)^2-4x^2y^2]=3(x^2+y^2-2xy)(x^2+y^2+2xy)=3(x+y)^2(x-y)^2
=3(x²-y²)²

答

=3[(x²+y²)²-4x²y²]
=3[(x^4+2x²y²+y^4-4x²y²]
=3(x²-y²)²