Question

关于“因式分解”的数学题,已知x^2-y^2-z^2=0,A是一个关于x,y,z的一次多项式,且x^3-y^3-z^3=

Answer 1

对x^3-y^3-z^3因式分解得：(x-y)(x^2+xy+y^2)-z^3

由已知得：x^2-y^2=z^2

所以：z^3=z*z^2=z(x^2-y^2)=z(x-y)(x+y)

故 (x-y)(x^2+xy+y^2)-z^3

=(x-y)(x^2+xy+y^2)-z(x-y)(x+y)

=(x-y)(x^2+xy+y^2-xz-yz)

=(x-y)[x(x-z)+y(x-z)]

=(x-y)(x-z)(x+y)

与等式右边比较可知：A=x+y