因式分解的.(x+1)(x+2)(x+3)(x+4)+1 ; 计算:100^2-99^2+98^2-97^2+……+2^2-1^2.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 17:34:24
![因式分解的.(x+1)(x+2)(x+3)(x+4)+1 ; 计算:100^2-99^2+98^2-97^2+……+2^2-1^2.](/uploads/image/z/744867-27-7.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E7%9A%84.%EF%BC%88x%2B1%29%28x%2B2%29%28x%2B3%29%28x%2B4%29%2B1+%3B+%E8%AE%A1%E7%AE%97%EF%BC%9A100%5E2-99%5E2%2B98%5E2-97%5E2%2B%E2%80%A6%E2%80%A6%2B2%5E2-1%5E2.)
因式分解的.(x+1)(x+2)(x+3)(x+4)+1 ; 计算:100^2-99^2+98^2-97^2+……+2^2-1^2.
因式分解的.
(x+1)(x+2)(x+3)(x+4)+1 ; 计算:100^2-99^2+98^2-97^2+……+2^2-1^2.
因式分解的.(x+1)(x+2)(x+3)(x+4)+1 ; 计算:100^2-99^2+98^2-97^2+……+2^2-1^2.
1.原式=[(x+1)(x+4)][(x+2)(x+3)]+1
=[x^2+5x+4][x^2+5x+6]+1
=(x^2+5x)^2+10(x^2+5x)+24+1
=(x^2+5x+5)^2
2.原式=(100+99)(100-99)+(98+97)(98-97)+...+(2+1)(2-1)
=100+99+98+97+...+2+1
=50(100+1)
=5050
(100-1)(100+1)-(99-2)(99+2)+。。。。。+(56-55)(56+55)
=101(99-98+97-96+。。。+1)
=101(50)
=5050
(x+1)(x+4) (x+2)(x+3) +1
(x^2+5x+4)(x^2+5x+6)+1
(x^2+5x)^2 + 10(x^2+5x) +25
(x^2+5x+5)^2
100^2-99^2+98^2-97^2+……+2^2-1^2.=(100+99)(100-99)+(98+97)(98-97)+....+(2+1)(2-1)=100+99+98+97+...+3=5047
=[(x+1)(x+4)][(x+2)(x+3)]+1
=[x^2+5x+4][x^2+5x+6]+1
=(x^2+5x)^2+10(x^2+5x)+24+1
=(x^2+5x+5)^2