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第67页

信息发布者：

-2023

$ \begin{aligned}解：原式&=2(m²-6m+9) \\ &=2(m-3)². \\ \end{aligned}$

$ \begin{aligned}解：原式&=a²+8a-9-8a \\ &=a²-9 \\ &=(a-3)(a+3). \\ \end{aligned}$

$ \begin{aligned}解：原式&=2a(x⁴-16y⁴) \\ &=2a(x²+4y²)(x²-4y²) \\ &= 2a(x²+4y²)(x+2y)(x-2y). \\ \end{aligned}$

$ \begin{aligned}解：原式&=(a²+b²)²-(2ab)² \\ &=[(a²+b²)+2ab][(a²+b²)-2ab] \\ &=(a+b)²(a-b)². \\ \end{aligned}$

$ \begin{aligned}解：原式&=-y(9x²-6xy+y²) \\ &=-y(3x-y)². \\ \end{aligned}$

$ \begin{aligned}解：原式&=[2(x+2y)-3x]² \\ &=(4y-x)². \\ \end{aligned}$

$ \begin{aligned}解：原式&=π(98²-4) \\ &=π(98+2)(98-2) \\ &=9600π \\ \end{aligned}$

$ \begin{aligned}解：原式&=(105-5)² \\ &=100² \\ &=10000. \\ \end{aligned}$

$ \begin{aligned}解：原式&=(1.22×3)²-(1.33×2)² \\ &=3.66²-2.66² \\ &=(3.66+2.66)(3.66-2.66) \\ &=6.32. \\ \end{aligned}$

（更多请查看作业精灵详解）

$ \begin{aligned} 解：原式&=(a²-2)(a²-4) \\ &=(a²-2)(a+2)(a-2). \\ \end{aligned}$

$ \begin{aligned} 解：原式&=x²+2x+3x+6 \\ &=x(x+2)+3(x+2) \\ &=(x+2)(x+3). \\ \end{aligned}$

$ \begin{aligned}解：原式&=(4m²+4m+1)-n² \\ &=(2m+1)²-n² \\ &=(2m+1+n)(2m+1-n). \\ \end{aligned}$

$ \begin{aligned}解：原式&=a⁴+4a²b²+4b⁴-4a²b² \\ &=(a²+2b²)²-(2ab)² \\ &=(a²+2b²+2ab)(a²+2b²-2ab). \\ \end{aligned}$

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

$~~~~~~~~~~~~~~~~~~~×(1-\frac{1}{4})×(1+\frac{1}{4})×···×(1-\frac{1}{2024})$

$~~~~~~~~~~~~~~~~~~~×(1+\frac{1}{2024}) $

$~~~~~~~~~~~~~~~~~~=\frac{1}{2}×(\frac{3}{2}×\frac{2}{3})× (\frac{4}{3}×\frac{3}{4})$

$~~~~~~~~~~~~~~~~~~~×···×(\frac{2024}{2023}×\frac{2023}{2024})×\frac{2025}{2024} $

$~~~~~~~~~~~~~~~~~~=\frac{1}{2}×\frac{2025}{2024} $

$~~~~~~~~~~~~~~~~~~=\frac{2025}{4048} $