因式分解x^4-4x^3+4x^2-1

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因式分解x^4-4x^3+4x^2-1
因式分解x^4-4x^3+4x^2-1

因式分解x^4-4x^3+4x^2-1
x^4-4x^3+4x^2-1
=(x^2-2x)^2-1
=(x^2-2x-1)(x^2-2x+1)
=(x^2-2x-1)(x-1)^2
=(x-1+√2)(x-1-√2)(x-1)^2

x^4-4x^3+4x^2-1
=x^4-x^3-3x^3+3x^2+x^2-1
=x^3(x-1)-3x^2(x-1)+(x+1)(x-1)
=(x-1)(x^3-3x^2+x+1)
=(x-1)[x^3-x^2-2x^2+2x-x+1]
=(x-1)[x^2(x-1)-2x(x-1)-(x-1)]
=(x-1)^2(x^2-2x-1)
=(x-1)^2(x^2-2x+1-2)
=(x-1)^2[(x-1)^2-2]
=(x-1)^2(x-1+√2)(x-1-√2)

x^4-4x^3+4x^2-1
=x^4-x^3-3x^3+3x^2+x^2-1
=x^3(x-1)-3x^2(x-1)+(x+1)(x-1)
=(x-1)(x³-3x²+x+1)
=(x-1)(x³-x²-2x²+2x-x+1)
=(x-1)[x²(x-1)-2x(x-1)-(x-1)]
=(x-1)²(x²-2x-1)

x^8-8x^8y^8-8y^8 =(x^8)^8-8×8x^8y^8-(8y)^8 =(x^8-8y)^8

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