写出计算结果:(x-1)(x+1)=______ (x-1)(x2+x+1)=______ (x-1)(x3
题型:解答题难度:一般来源:不详
写出计算结果:(x-1)(x+1)=______ (x-1)(x2+x+1)=______ (x-1)(x3+x2+x+1)=______ 根据以上等式进行猜想,可得:(x-1)(xn+xn-1+…+x+1)=______. |
答案
(x-1)(x+1)=x2-1; (x-1)(x2+x+1)=x3-1; (x-1)(x3+x2+x+1)=x4-1; 猜想:(x-1)(xn+xn-1+…+x+1)=xn+1-1; 故答案为:x2-1,x3-1,x4-1,xn+1-1. |
举一反三
计算:(a-2b)(-a-2b)=______; (-a-2a2)2=______. |
下列各式可以用平方差公式计算的是( )A.(x-y)(-x+y) | B.(2m+3n)(3m-2n) | C.(4a+9b)(9b-4a) | D.(t-4)(4-t) |
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现有下列算式 (1)(x+y)(x-y) (2)(x+y)(y-x) (3)(-x-y)(x+y) (4)(-x+y)(x-y) 其中满足平方差公式的有( ) |
计算: ①29.8×30.2; ②46×512; ③2052. |
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