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第69页

信息发布者：

2b(b-1)²

100

$解：$

$ \begin{aligned}(1)原式&=a(b²-9) \\ &=a(b+3)(b-3). \\ (2)原式&=3(x²-4ax+4a²) \\ &=3(x-2a)². \\ (3)原式&=-a(a²-2ab+b²) \\ &=-a(a-b)². \\ \end{aligned}$

$解：x³+2x+3$

$ =x³-x+3x+3$

$ =x(x²-1)+3(x+1)$

$ =x(x+1)(x-1)+3(x+1)$

$ =(x+1)(x²-x+3).$

$解：x⁴-3x²+1$

$ =x⁴-2x²+1-x²$

$ =(x²-1)²-x²$

$ =(x²+x-1)(x²-x-1).$

$解：$

$ \begin{aligned}(1)原式&=(2022-2)(2022+2)-2022² \\ &=2022²-2²-2022² \\ &=-4. \\ (2)原式&=-1×1-(\frac{1}{-8}) \\ &=-1+\frac{1}{8} \\ &=-\frac{7}{8}. \\ (3)原式&=9x²-4-5x²+5x-4x²+4x-1 \\ &=9x-5. \\ \end{aligned}$

$ ∴x=-\frac{1}{3}, $

$∴9x-5=9×(-\frac{1}{3})-5=-8.$

$解：(1)x⁴+4y⁴\ $

$=x⁴+4x²y²+4y²-4x²y²$

$=(x²+2y²)²-4x²y²\ $

$=(x²+2y²+2xy)(x²+2y²-2xy).$

$(2)x²-2ax-b²-2ab$

$ =x²-2ax+a²-a²-b²-2ab$

$=(x-a)²-(a+b)²$

$ =(x-a+a+b)(x-a-a-b)$

$ =(x+b)(x-2a-b).$