1)x9+x6+x3-3；
(2)(m2-1)(n2-1)+4mn；
(3)(x+1)4+(x2-1)2+(x-1)4；
(4)a3b-ab3+a2+b2+1．
解 (1)将-3拆成-1-1-1．
原式=x9+x6+x3-1-1-1
=(x9-1)+(x6-1)+(x3-1)
=(x3-1)(x6+x3+1)+(x3-1)(x3+1)+(x3-1)
=(x3-1)(x6+2x3+3)
=(x-1)(x2+x+1)(x6+2x3+3)．
(2)将4mn拆成2mn+2mn．
原式=(m2-1)(n2-1)+2mn+2mn
=m2n2-m2-n2+1+2mn+2mn
=(m2n2+2mn+1)-(m2-2mn+n2)
=(mn+1)2-(m-n)2
=(mn+m-n+1)(mn-m+n+1)．
(3)将(x2-1)2拆成2(x2-1)2-(x2-1)2．
原式=(x+1)4+2(x2-1)2-(x2-1)2+(x-1)4
=〔(x+1)4+2(x+1)2(x-1)2+(x-1)4]-(x2-1)2
=〔(x+1)2+(x-1)2]2-(x2-1)2
=(2x2+2)2-(x2-1)2=(3x2+1)(x2+3)．
(4)添加两项+ab-ab．
原式=a3b-ab3+a2+b2+1+ab-ab
=(a3b-ab3)+(a2-ab)+(ab+b2+1)
=ab(a+b)(a-b)+a(a-b)+(ab+b2+1)
=a(a-b)〔b(a+b)+1]+(ab+b2+1)
=[a(a-b)+1](ab+b2+1)
=(a2-ab+1)(b2+ab+1)．