已知x≠1,计算(1+x)(1-x)=1-x^2,(1-x)(1+x+x^2)=1-x^3,(1-x)(1+x+x^2+x^3)=1-x^4.(1)(1-2)(1+2+2^2+2^3+2^4+2^5)=(2)2+2^2+2^3+2^4+...+2^n= (n>0)(3)(x-1)(x^99+x^98+x^97+...+x^2+x+1)=探索规律:(1)(a-b)(a+b)=(2)(a-b)(a^2+ab+b^2)=(3)(a-b)(a^3+a^2 *b+a*b
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/13 13:44:52
![已知x≠1,计算(1+x)(1-x)=1-x^2,(1-x)(1+x+x^2)=1-x^3,(1-x)(1+x+x^2+x^3)=1-x^4.(1)(1-2)(1+2+2^2+2^3+2^4+2^5)=(2)2+2^2+2^3+2^4+...+2^n= (n>0)(3)(x-1)(x^99+x^98+x^97+...+x^2+x+1)=探索规律:(1)(a-b)(a+b)=(2)(a-b)(a^2+ab+b^2)=(3)(a-b)(a^3+a^2 *b+a*b](/uploads/image/z/3138142-22-2.jpg?t=%E5%B7%B2%E7%9F%A5x%E2%89%A01%2C%E8%AE%A1%E7%AE%97%281%2Bx%29%281-x%29%3D1-x%5E2%2C%281-x%29%281%2Bx%2Bx%5E2%29%3D1-x%5E3%2C%281-x%29%281%2Bx%2Bx%5E2%2Bx%5E3%29%3D1-x%5E4.%281%29%281-2%29%281%2B2%2B2%5E2%2B2%5E3%2B2%5E4%2B2%5E5%29%3D%282%292%2B2%5E2%2B2%5E3%2B2%5E4%2B...%2B2%5En%3D+%28n%3E0%29%283%29%28x-1%29%28x%5E99%2Bx%5E98%2Bx%5E97%2B...%2Bx%5E2%2Bx%2B1%29%3D%E6%8E%A2%E7%B4%A2%E8%A7%84%E5%BE%8B%3A%281%29%28a-b%29%28a%2Bb%29%3D%282%29%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%3D%283%29%28a-b%29%28a%5E3%2Ba%5E2+%2Ab%2Ba%2Ab)
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