作业帮(-x^2+2x-4)(-x^2+2x+2)+9
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/11 16:11:27
(-x^2+2x-4)(-x^2+2x+2)+9
(-x^2+2x-4)(-x^2+2x+2)+9
(-x^2+2x-4)(-x^2+2x+2)+9
令-x²+2x=a
原式=(a-4)(a+2)+9
=a²-2a-8+9
=a²-2a+1
=(1-a)²
=(1+x²-2x)²
=(x-1)⁴
(-x^2+2x-4)(-x^2+2x+2)+9
=(x^2-2x+4)(x^2-2x-2)+9
=[(x^2-2x)+4][(x^2-2x)-2]+9
=(x^2-2x)^2+2(x^2-2x)-8+9
=(x^2-2x)^2+2(x^2-2x)+1
=[(x^2-2x)+1]^2
=(x^2-2x+1)^2
=[(x-1)^2]^2
=(x-1)^4
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