x4-2(a2+b2)x2+(a2-b2)2因式分解

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x4-2(a2+b2)x2+(a2-b2)2因式分解x4-2(a2+b2)x2+(a2-b2)2因式分解x4-2(a2+b2)x2+(a2-b2)2因式分解原式=x^4-2﹙a²+b

x4-2(a2+b2)x2+(a2-b2)2因式分解
x4-2(a2+b2)x2+(a2-b2)2因式分解

x4-2(a2+b2)x2+(a2-b2)2因式分解
原式=x^4-2﹙a²+b²﹚x²+﹙a²+b²﹚²-4a²b²
=﹙x²-a²-b²﹚²-﹙2ab﹚²
=﹙x²-a²-b²-2ab﹚﹙x²-a²-b²+2ab﹚
=[x²-﹙a+b﹚²][x²-﹙a-b﹚²]
=﹙x-a-b﹚﹙x+a+b﹚﹙x-a+b﹚﹙x+a-b﹚

x4-2(a2+b2)x2+(a2-b2)2
=(x^2-a^2-b^2)^2-(2ab)^2
=(x^2-a^2-b^2-2ab)(x^2-a^2-b^2+2ab)
=[x^2-(a+b)^2][x^2-(a-b)^2]
=(x-a-b)(x+a+b)(x-a+b)(x+a-b) .

〔x2-a2-b2〕2