Question

分解因式（a²+b²）²-（2ab）² （x+y）²-2(x²-y²)+（x-y）²

Answer 1

(a²+b²)²-(2ab)²
=[(a²+b²)+2ab][(a²+b²)-2ab]
=(a²+2ab+b²)(a²-2ab+b²)
=(a+b)²(a-b)²

(x+y)²-2(x²-y²)+(x-y)²
=(x+y)²-2(x+y)(x-y)+(x-y)²
=[(x+y)-(x-y)]²
=(2y)²
=4y²

Answer 2

答：
（a²+b²）²-（2ab）²
=(a²+b²-2ab)(a²+b²+2ab)
=(a-b)(a-b)(a+b)(a+b)

（x+y）²-2(x²-y²)+（x-y）²
=x²+2xy+y²-2x²+2y²+x²-2xy+y²
=4y²

Answer 3

（a²+b²）²-（2ab）²
＝﹙a²＋b²＋2ab﹚﹙a²＋b²－2ab﹚
＝﹙a＋b﹚²﹙a－b﹚²

（x+y）²-2(x²-y²)+（x-y）²
＝（x+y）²-2(x＋y)﹙x－y﹚+（x-y）²
＝[(x＋y)－(x－y)]²
＝﹙x＋y－x＋y﹚²
＝(2y)²
＝4y²

求采纳~~~~~~~~~