(x^2-2x-2)(x^2-2x+4)+9(分解因式)

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(x^2-2x-2)(x^2-2x+4)+9(分解因式)

(x^2-2x-2)(x^2-2x+4)+9(分解因式)
(x^2-2x-2)(x^2-2x+4)+9(分解因式)

(x^2-2x-2)(x^2-2x+4)+9(分解因式)
设 x^2 - 2x = y
原式= (y-2)(y+4)+9
= y^2 + 2y - 8 + 9
= y^2 + 2y + 1
= (y+1)^2
= (x^2 - 2x + 1)^2
= (x-1)^4
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(x^2-2x-2)(x^2-2x+4)+9
=(x^2-2x)^2+2(x^2-2x)+1
=(x^2-2x+1)^2
=(x-1)^4

=(x-1)^4
=x^4-4x^3+6x^2-4X+1

=(x^2-2x)^2+2(x^2-2x)+1=(x^2-2x+1)^2=(x-1)^4

原式=x^2-2x)^2+2(x^2-2x)+1
=(x^2-2x+1)^2
=(x-1)^4
知道了不??
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