分解因式(x²+y²)³+(z²-x²)³-(y²+z²)³=

来源：学生作业帮助网编辑：六六作业网时间：2024/11/25 01:25:15

分解因式(x²+y²)³+(z²-x²)³-(y²+z²)³=分解因式(x²+y²)

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)