x^4+y^4
=x^4+y^4+2x^2y^2-2x^2y^2
=(x^2+y^2)^2-2x^2y^2
=(x^2+y^2-2^1/2xy)(x^2+y^2+2^1/2xy)好搞笑的问题哈,上面的就是答案了
加一个2X²Y²再减一个2X²Y²就可以写成(X²+Y²)²-2 X²Y²。再用平方差公式配方就可以了。
解:
A=x*x*x*x+y*y*y*y=x*x*x*x+2x*x*y*y+y*y*y*y-2x*x*y*y
=(x*x+y*y)(x*x+y*y)-2x*x*y*y
=(x*x+y*y+x*y*根号2)(x*x+y*y-x*y*根号2)
X4+y4=x4+2x2y2+y4-2x2y2=(x2+y2)2-(21/2xy)2=(x2+y2+21/2xy)(x2+y2-21/2xy)