x的四次方+2x²y²+y的四次方-4x²y²【因式分解】

x的四次方+2x²y²+y的四次方-4x²y²【因式分解】
x的四次方+2x²y²+y的四次方-4x²y²【因式分解】

x的四次方+2x²y²+y的四次方-4x²y²【因式分解】
解
x^4++2x²y²+y^4-4x²y²
=(x²+y²)²-(2xy)²
=[(x²+y²)-2xy][(x²+y²)+2xy]
=(x-y)²(x+y)²

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

x的四次方+2x²y²+y的四次方-4x²y²
=x的四次方-2x²y²+y的四次方
=(x²-y²)²
=(x+y)²(x-y)²

答：
x的四次方+2x²y²+y的四次方-4x²y²
=x^4+2x²y²+y^4-4x²y²
=x^4-2x²y²+y^4
=(x²-y²)²
=(x-y)²(x+y)²