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1.=(x³-1)-(11x²-31x+20)
=(x-1)(x²+x+1)-(11x-20)(x-1)
=(x-1)(x²+x+1-11x+20)
=(x-1)(x²-10x+21)
=(x-1)(x-3)(x-7)
2.=(x-2m)²-4(m²-2mn+n²)
=(x-2m)²-4(m-n)²
=(x-4m+2n)(x-2n)
=(x-1)(x²+x+1)-(11x-20)(x-1)
=(x-1)(x²+x+1-11x+20)
=(x-1)(x²-10x+21)
=(x-1)(x-3)(x-7)
2.=(x-2m)²-4(m²-2mn+n²)
=(x-2m)²-4(m-n)²
=(x-4m+2n)(x-2n)
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展开全部
(1) x^3-11x^2+31x-21
=(x^3-x^2)-(10x^2-10x)+(21x-21)
=x^2(x-1)-10x(x-1)+21(x-1)=(x-1)(x^2-10x+21)=(x-1)(x-3)(x-7)
(2) x^2-4mx+8mn-4n^2
=(x^2-4n^2)-(4mx-8mn)=(x+2n)(x-2n)-4m(x-2n)=(x-2n)(x+2n-4m)
=(x^3-x^2)-(10x^2-10x)+(21x-21)
=x^2(x-1)-10x(x-1)+21(x-1)=(x-1)(x^2-10x+21)=(x-1)(x-3)(x-7)
(2) x^2-4mx+8mn-4n^2
=(x^2-4n^2)-(4mx-8mn)=(x+2n)(x-2n)-4m(x-2n)=(x-2n)(x+2n-4m)
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