神马作文网因式分解:1)1-2^2+3^2-4^2+5^2-6^2+...+99^2-100^2; 2)(2+1)(2^2+1)(
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/16 18:13:11
因式分解:1)1-2^2+3^2-4^2+5^2-6^2+...+99^2-100^2; 2)(2+1)(2^2+1)(2^4+1)(2^8+1
1-2^2+3^2-4^2+5^2-6^2+...+99^2-100^2
=(1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+...+(99-100)(99+100)
=-1-2-3-4-...-100
=(-1-100)*100/2
=-5050
(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)
=(2^4-1)(2^4+1)(2^8+1)
=(2^8-1)(2^8+1)
=2^16-1
=(1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+...+(99-100)(99+100)
=-1-2-3-4-...-100
=(-1-100)*100/2
=-5050
(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)
=(2^4-1)(2^4+1)(2^8+1)
=(2^8-1)(2^8+1)
=2^16-1