Question

n是正整数,化简(-x^2)^n+(-x^n)^2+x^2n

Answer 1

(-x^2)^n+(-x^n)^2+x^2n

当n为奇数时：

(-x^2)^n+(-x^n)^2+x^2n

=-x^2n+x^2n+x^2n

=x^2n

当n为偶数时：

(-x^2)^n+(-x^n)^2+x^2n

=x^2n+x^2n+x^2n

=3x^2n