(1+a²+b²-2a)²-(4b-4ab)(1+a²-b²-2a)
解:原式=[﹙1+a²-2a﹚+b²]²-4b﹙1-a﹚[﹙1+a²-2a﹚-b²]
=[﹙a-1﹚²+b²]²+4b﹙a-1﹚[﹙a-1﹚²-b²]
设 a-1=u
=﹙u²+b²﹚²+4bu﹙u²-b²﹚
=﹙u²-b²﹚²+4b²u²+4bu﹙u²-b²﹚
=﹙u²-b²﹚²+2×2bu﹙u²-b²﹚+﹙2bu﹚²
=﹙u²-b²+2bu﹚²
=[﹙a-1﹚²-b²+2b﹙a-1﹚]²
=﹙a²-2a+1-b²+2ab-2b﹚²
=﹙a²+2ab-b²-2a-2b+1﹚²
12x^3+16x²-5x-3
解:原式=12x^3+16x-3x-2x-3
=x﹙6x-1﹚﹙2x+3﹚-﹙2x+3﹚
=﹙6x²-x﹚﹙2x+3﹚-﹙2x+3﹚
=﹙6x²-x-1﹚﹙2x+3﹚
=﹙2x-1﹚﹙3x+1﹚﹙2x+3﹚
x^6-2x^4+6x^3+x²﹣6x+9
解:原式=x^6-2x³﹙x-3﹚+﹙x²-6x+9﹚
=x^6-2x³﹙x-3﹚+﹙x-3﹚²
=[x³-﹙x-3﹚]²
=﹙x³-x+3﹚²
9c²﹙a+c﹚﹙a-c﹚-b﹙b+6c²﹚
解:原式=9c²﹙a²-c²﹚-b﹙b+6c²﹚
=9a²c²-9c^4-b²-6bc²
=9a²c²-﹙9c^4+b²+6bc²﹚
=9a²c²-[﹙3c²﹚²+b²+2×b×3c²]
=9a²c²-﹙3c²+b﹚²
=﹙9a²c²-3c²-b²﹚﹙9a²c²+3c²+b﹚
第3题楼主少写了一项:正确的题目应该是;x^6-2x^4+6x^3+x²﹣6x+9
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