第75页 - 经纶学典学霸七年级数学上下册【江苏国标】

A

40

a²-b²

(a+b)(a-b)

(a+b)(a-b)=a²-b²

(a+b)³=a³+b³+3a²b+3ab²

133

9

(x+1)(x-1)x=x³-x

（更多请点击查看作业精灵详解）

$解：2×(1+\frac{1}{2})×(1+\frac{1}{2^2})×(1+\frac{1}{2^4})×(1+\frac{1}{2^8})+\frac{1}{2^{14}}$

$=4×(1-\frac{1}{2})×(1+\frac{1}{2})×(1+\frac{1}{2^2})×(1+\frac{1}{2^4})×(1+ \frac{1}{2^8})+\frac{1}{2^{14}}$

$=4×(1\frac{1}{2²}) ×(1+\frac{1}{2^2})×(1+\frac{1}{2^4})×(1+ \frac{1}{2^8})+\frac{1}{2^{14}}$

$=4×(1-\frac{1}{2^4}) ×(1+\frac{1}{2^4})×(1+ \frac{1}{2^8})+\frac{1}{2^{14}}\ $

$=4×(1-\frac{1}{2^8})×(1+ \frac{1}{2^8})+\frac{1}{2^{14}}\ $

$=4×(1-\frac{1}{2^{16}}+\frac{1}{2^{14}} =4-\frac{1}{2^{14}}+\frac{1}{2^{14}}$

$=4$