将多项式x四次方+y四次方+z四次方-2x²y²-2x²z²-2y²z²分解因式.

问题描述:

将多项式x四次方+y四次方+z四次方-2x²y²-2x²z²-2y²z²分解因式.

原式=X^4-2X²Y²+Y^4-2(X²-Y²)Z²+Z^4
=(X²-Y²)²-2(X²-Y²)Z²+Z^4
=(X²-Y²-Z²)²