第77页 - 经纶学典学霸七年级数学上下册【江苏国标】

$ \begin{aligned}解：原式&=x²-2×70x+70²-70²+4875 \\ &=(x-70)²-25 \\ &=(x-70)²-5² \\ &=(x-70+5)(x-70-5) \\ &=(x-65)(x-75) \\ \end{aligned}$

$ \begin{aligned}解：原式&=(2x)²-2×2x×1+1²-1²-575 \\ &=(2x-1)²-576 \\ &=(2x-1)²-24² \\ &=(2x-1+24)(2x-1-24) \\ &=(2x+23)(2x-25) \\ \end{aligned}$

$ \begin{aligned}解：原式&=x⁴+4x²y²+4y⁴-4x²y² \\ &=(x²+2y²)²-(2xy)² \\ &=(x²+2y²+2xy)(x²+2y²-2xy) \\ \end{aligned}$

$ \begin{aligned}解：原式&=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) \\ \end{aligned}$

（更多请点击查看作业精灵详解）

$解：解法一(拆二次项):$

$ \begin{aligned}原式&=(x³+x²)+(x²-5x-6) \\ &=x²(x+1)+(x+ 1)(x-6) \\ &=(x+1)(x²+x-6) \\ &=(x+1)(x-2)(x+3) \\ \end{aligned}$

$解法二(拆一次项):$

$ \begin{aligned}原式&=(x³+2x²-8x)+(3x-6) \\ &=x(x²+2x-8)+3(x-2) \\ &=x(x-2)(x+4)+3(x-2) \\ &=(x-2)(x²+4x+3) \\ &=(x-2)(x+1)(x+3) \\ \end{aligned}$

$解法三(拆常数项):$

$ \begin{aligned}原式&=(x³+1)+(2x²-5x-7) \\ &=(x+1)(x²-x+1)+(x+1)(2x-7) \\ &=(x+1)(x²-x+1+2x-7) \\ &=(x+1)(x²+x-6) \\ &=(x+1)(x-2)(x+3) \\ \end{aligned}$

$解法四(拆二次项与一次项):$

$ \begin{aligned}原式&=(x³+x²)+(x²+x)-(6x+6) \\ &=x²(x+1)+x(x+1)-6(x+1) \\ &=(x+1)(x²+x-6) \\ &=(x+1)(x-2)(x+3) \\ \end{aligned}$