分解下列因式：（1）a²-b²+a-b（2）3ax-4by-4ay+3bx(3)3a³+6a²b-3a²c-6abc(4)(x+1)²-(y-3)²(5)4(x+y)²-16(a-b)²(6)(x²-3x)²-2(x²-3x)-8(7)x(x+3)(x+2)(x+1)+1

Question

分解下列因式：
（1）a²-b²+a-b
（2）3ax-4by-4ay+3bx
(3)3a³+6a²b-3a²c-6abc
(4)(x+1)²-(y-3)²
(5)4(x+y)²-16(a-b)²
(6)(x²-3x)²-2(x²-3x)-8
(7)x(x+3)(x+2)(x+1)+1

Answer 1

（1）a²-b²+a-b=(a-b)(a+b)+(a-b)=(a-b)(a+b+1);
（2）3ax-4by-4ay+3bx=3x(a+b)-4y(a+b)=(a+b)(3x-4y);
(3)3a³+6a²b-3a²c-6abc=3a²(a-c)+6ab(a-c)=3a(a-c)(a+2b);
(4)(x+1)²-(y-3)²=(x+1+y-3)(x+1-y+3)=(x-y-2)(x-y+4);
(5)4(x+y)²-16(a-b)²=[2(x+y)+4(a-b)][2(x+y)-4(a-b)]=4(x+y+2a-2b)(x+y-2a+2b);
(6)(x²-3x)²-2(x²-3x)-8=(x²-3x)²-2(x²-3x)+1-9=[(x²-3x)-1]²-9=[(x²-3x)-1+3][(x²-3x)-1-3]=(x²-3x+2)(x²-3x-4)=(x-1)(x-2)(x+1)(x-4);