第61页 - 经纶学典学霸七年级数学上下册【江苏国标】

±3

10

120

$ 解：原式=(40+\frac{1}{3} ×(\frac{1}{3}-40) $

$~~~~~~~~~~~~~~~~~=(\frac{1}{3})² -40² $

$~~~~~~~~~~~~~~~~~=\frac{1}{9}-1600 $

$~~~~~~~~~~~~~~~~~= -1599\frac{8}{9} $

$ \begin{aligned}解：原式&=2022²-(2022-1)×(2022+1) \\ &=2022²-2022²+1 \\ &=1. \\ \end{aligned}$

$解：原式=\frac{1}{5}×7.35²-\frac{1}{5}×25×1.07²$

$~~~~~~~~~~~~~~~~~=\frac{1}{5}×(7.35²-5²×1.07²)$

$~~~~~~~~~~~~~~~~~= \frac{1}{5}×(7.35²-5.35²)$

$~~~~~~~~~~~~~~~~~=\frac{1}{5}×(7.35-5.35)×(7.35+5.35)$

$~~~~~~~~~~~~~~~~~=\frac{1}{5}×2×12.7$

$~~~~~~~~~~~~~~~~~=5.08.$

（更多请点击查看作业精灵详解）

6

1

$ \begin{aligned}解：原式&=(3-1)×(3+1)×(3^2+1)×(3^4+1)×(3^8+1)+1 \\ &=(3^2-1)×(3^2+1)×(3^4+1)×(3^8+1)+1 \\ &=(3^4-1)×(3^4+1)×(3^8+1)+1 \\ &=(3^8-1)×(3^8+1)+1 \\ &=3^{16} \\ \end{aligned}$

$解：原式=(1-\frac{1}{2})×(1+\frac{1}{2})×(1-\frac{1}{3})×(1+\frac{1}{3})×(1- \frac{1}{4})×(1+\frac{1}{4})×···×(1-\frac{1}{10})×(1+\frac{1}{10})$

$=\frac{1}{2}×\frac{3}{2}×\frac{2}{3}×\frac{4}{3}×\frac{3}{4}×\frac{5}{4}×···×\frac{9}{10}×\frac{11}{10}$

$=\frac{1}{2}×\frac{11}{10}$

$=\frac{11}{20}$

$解：原式=(100+99)×(100-99)+(98+97)×(98-97)+···+(4+3)×(4-3)+(2+1)×(2-1)$

$=100+99+98+97+···+4+3+2+1$

$=5050.$