(3^n+5^n)^2-(9^n+25^n)(n为正整数)

来源：学生作业帮助网编辑：六六作业网时间：2024/12/24 00:57:31

(3^n+5^n)^2-(9^n+25^n)(n为正整数)(3^n+5^n)^2-(9^n+25^n)(n为正整数)(3^n+5^n)^2-(9^n+25^n)(n为正整数)=9^n+2×3^n×5^

(3^n+5^n)^2-(9^n+25^n)(n为正整数)
(3^n+5^n)^2-(9^n+25^n)(n为正整数)

(3^n+5^n)^2-(9^n+25^n)(n为正整数)
=9^n+2×3^n×5^n+25^n-9^n-25^n
=2×15^n

3^2n+5^2n+15^n乘以2-9^n-25^n=9^n+25^n-9^n-25^n+15^n乘以2=15^n乘以2