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1、因式分解: 1 x^(n+5)+9x^(n+3)-162x^(n+1) 2 (x^2+5x+6)(x^2+5x-2)+16 其他: 3 (-2)^99+(-2)^100=2^n, 求n. 4 化简 84a^2 b^3 c^4 d^2 ----------------- =______ ; -96c^2 d^3 b^5 a 2xy-x^2-y^2+z^2 --------------- =______ 2xz+x^2-y^2+z^2 a^2 a^3-1 5 计算:(-a^2+ --- -a-1)* ----- a-1 a^2+a+11. x^(n+5)+9x^(n+3)-162x^(n+1) =x^(n+1)(x^4+9x²-162) =x^(n+1)(x²+18)(x²-9) =x^(n+1)(x²+18)(x+3)(x-3) 2. (x²+5x+6)(x²+5x-2)+16 =(x²+5x+2+4)(x²+5x+2-4)+16 =(x²+5x+2)²-16+16 =(x²+5x+2)² 3. 2^n=(-2)^99+(-2)^100 =2^100-2^99 =2^99*(2-1)=2^99， 故n=99。

2、 4. (84a²b³c^4 d²)/(-96c²d³b^5 a ) =-(7ac²)/(8b²d) (2xy-x²-y²+z²)/(2xz+x²-y²+z²) =[z²-(x-y)²]/[(x+z)²-y²] =[(x-y+z)(-x+y+z)]/[(x-y+z)(x+y+z)] =(y+z-x)/(x+y+z) 5. [-a²+a²/(a-1)-a-1]*(a³-1)/(a²+a+1) =a²*(a³-1)/[(a²+a+1)(a-1)]+(-a²-a-1)*(a³-1)/(a²+a+1) =a²-(a³-1) = -a³+a²+1。

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