一道初中de 数学题x^4+y^4+z^4-2(xy)^2-2(xz)^2-2(yz)^2分解因式
2019-05-07
一道初中de 数学题
x^4+y^4+z^4-2(xy)^2-2(xz)^2-2(yz)^2
分解因式
优质解答
=[x^4+y^4-2(xy)^2]+z^4-2(xz)^2-2(yz)^2
=(x^2-y^2)^2+z^4-2(x^2-y^2)z^2-4(yz)^2
=(x^2-y^2-z^2)^2-(2yz)^2
=(x^2-y^2-z^2+2yz)(x^2-y^2-z^2-2yz)
=[x^4+y^4-2(xy)^2]+z^4-2(xz)^2-2(yz)^2
=(x^2-y^2)^2+z^4-2(x^2-y^2)z^2-4(yz)^2
=(x^2-y^2-z^2)^2-(2yz)^2
=(x^2-y^2-z^2+2yz)(x^2-y^2-z^2-2yz)