作业帮分解因式(x²+y²)³+(z²-x²)³-(y²+z²)³=
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/11 12:45:59
分解因式(x²+y²)³+(z²-x²)³-(y²+z²)³=
分解因式(x²+y²)³+(z²-x²)³-(y²+z²)³=
分解因式(x²+y²)³+(z²-x²)³-(y²+z²)³=
(x²+y²)³+(z²-x²)³-(y²+z²)³
= [(x²+y²)+(z²-x²)][(x²+y²)²+(z²-x²)²-(x²+y²)(z²-x²)]-(y²+z²)³
= （y²+z²）[(x²+y²)²+(z²-x²)²-(x²+y²)(z²-x²)]-(y²+z²)³
= （y²+z²）[(x²+y²)²+(z²-x²)²-(x²+y²)(z²-x²)-(y²+z²)²]
= （y²+z²）[(x²+y²-y²-z²）（x²+y²+y²+z²）+（z²-x²）（z²-x²-x²-y²）]
=（y²+z²）[(x²-z²)(x²+2y²+z²)+（z²-x²）（z²-2x²-y²）]
=（y²+z²）[(x²-z²)(x²+2y²+z²-z²+2x²+y²]
=3(y²+z²)(x²-z²)(x²+y²)
