因式分解怎么做啊?急!

发布网友发布时间：2024-10-14 09:16

共2个回答

热心网友时间：2024-10-14 09:44

原式=(x+y)^4+[(x+y)(x-y)]²+(x-y)^4
=(x+y)^4+2[(x+y)(x-y)]²+(x-y)^4-[(x+y)(x-y)]²
=[(x+y)²＋(x-y)²]²-[(x+y)(x-y)]²
=【2x²＋2y²】²-【x²-y²】²
=[2x²＋2y²-x²＋y²][2x²＋2y²+x²-y²]
=(x²＋3y²)(3x²＋y²)

热心网友时间：2024-10-14 09:43

原式=（x+y)^4+(x+y)²(x-y)²+(x-y)^4
=（x+y)^4+2(x+y)²(x-y)²+(x-y)^4-(x+y)²(x-y)²
=[(x+y)²+(x-y)²]²-(x+y)²(x-y)²
=[(x+y)²+(x-y)²+(x+y)(x-y)][(x+y)²+(x-y)²-(x+y)(x-y)]
=(x²+2xy+y²+x²-2xy+y²+x²-y²)(x²+2xy+y²+x²-2xy+y²-x²+y²)
=(3x²+y²)(x²+3y²)

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