利用因式分解计算:1+24×﹙5²+1﹚﹙5⁴+1﹚﹙5⁴×5⁴+1﹚

问题描述:

利用因式分解计算:1+24×﹙5²+1﹚﹙5⁴+1﹚﹙5⁴×5⁴+1﹚

1+24×(5^2+1)(5^4+1)(5^4×5^4+1)
=1+(5^2-1)(5^2+1)(5^4+1)(5^4×5^4+1)
=1+(5^4-1) (5^4+1)(5^4×5^4+1)
=1+(5^4×5^4-1) (5^4×5^4+1)
=1+5^16-1
=5^16