Question

1、因式分解：x²-2xy+y²-2x+2y+1 2、因式分解：-x的n+1次方+2x的n次方-x的n-1次方

3、计算:1998×2000-1999² 4、计算 [ 三分之一(x+1)的四次方]的三次方×[-3（x+1）²]三次方（结果用幂的形式表示)

Answer 1

x²-2xy+y²-2x+2y+1
=(x-y)²-2(x-y)+1
=(x-y-1)²

-x^(n+1)+2x^n-x^(n-1)
=-x^(n-1)*x^2+2x^(n-1)*x-x^(n-1)
=-x^(n-1)[x^2-2x+1]
=-x^(n-1)(x-1)^2

1998×2000-1999²
=(1999-1)(1999+1)-1999²
=1999²-1-1999²
=-1

[ 三分之一(x+1)的四次方]的三次方×[-3（x+1）²]三次方
=[1/3*(x+1)^4]^3×[-3（x+1）²]^3
=1/27*(x+1)^12×[-27（x+1）^6
=-1*(x+1)^18
=-(x+1)^18

Answer 2

x²-2xy+y²-2x+2y+1
=(x-y)²-2(x-y)+1
=(x-y-1)²

-x^(n+1)+2x^n-x^(n-1)
=-x^(n-1)*x^2+2x^(n-1)*x-x^(n-1)
=-x^(n-1)[x^2-2x+1]
=-x^(n-1)(x-1)^2

1998×2000-1999²
=(1999-1)(1999+1)-1999²
=1999²-1-1999²
=-1

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