5、分解因式：16(x2+4x+4)2·(x2-2x+1)2-(x2-6x+9)2.6、因式分解：4xy+2y-8x-y2

题目

5、分解因式：16(x2+4x+4)2·(x2-2x+1)2-(x2-6x+9)2.6、因式分解：4xy+2y-8x-y2

答案

16(x2+4x+4)2·(x2-2x+1)2-(x2-6x+9)2
=16(x+2)4*(x-1)4-(x-3)4
=[2(x+2)(x-1)]4-(x-3)4
={[2(x+2)(x-1)]2-(x-3)2}*{[2(x+2)(x-1)]2+(x-3)2}
=[4(x2+x-2)2-(x-3)2]* {[2(x+2)(x-1)]2+(x-3)2}
=(2x2+3x-7)(2x-1)(x+1) {[2(x+2)(x-1)]2+(x-3)2}
4xy+2y-8x-y2
=4x(y-2)-y(y-2)
=(4x-y)(y-2)