因式分解(1-m2)x2-4mx-(1-m2)

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因式分解(1-m2)x2-4mx-(1-m2)
因式分解(1-m2)x2-4mx-(1-m2)

因式分解(1-m2)x2-4mx-(1-m2)
(1-m2)x2-4mx-(1-m2)
=x2-x2m2-4mx-1+m2
=(x2-2mx+m2)-((xm)2+2mx+1)
=(x-m)2-(xm+1)2
=(x-m+xm+1)(x-m-xm-1)

(1-m2)x2-4mx-(1-m2)=﹙1-m²﹚﹙x²-4mx﹚

=x2-x2m2-4mx-1+m2
=(x2-2mx+m2)-((xm)2+2mx+1)
=(x-m)2-(xm+1)2
=(x-m+xm+1)(x-m-xm-1)