因式分解：(1)(x+3)^2-(3x+9)
问题描述：
因式分解：(1)(x+3)^2-(3x+9)
(2) x(6m-nx)-nx^2 (3) 2-5(3x-2)^2+3x (4) x(b+c-d)-y(d-b-c)-b-c+d (5) (4a-5b)(3m-2p)+(4b-a)(3m-2p)
(6) ab(x-2y)-ac(2y-x)+ab(2x-4y) (7) (a-b)^2(a+b)^3-(b-a)^2(b+a)^2
答
(1)(x+3)^2-(3x+9)
=(x+3)^2-3(x+3)
=(x+3)(x+3-3)
=x(x+3)
(2) x(6m-nx)-nx^2
=x[(6m-nx)-nx]
=x(6m-2nx)
(3) 2-5(3x-2)^2+3x
=2-45x²+60x-20+3x
=-45x²+63x-18
=-9(5x²-7x+2)
=-9(5x-2)(x-1)
(4) x(b+c-d)-y(d-b-c)-b-c+d
=x(b+c-d)+y(b+c-d)-(b+c-d)
=(x+y-1)(b+c-d)
(5) (4a-5b)(3m-2p)+(4b-a)(3m-2p)
=(3m-2p)(4a-5b+4b-a)
=(3m-2p)(3a-b)
(6) ab(x-2y)-ac(2y-x)+ab(2x-4y)
=ab(x-2y)+ac(x-2y)+2ab(x-2y)
=a(x-2y)(b+c-2b)
=a(x-2y)(c-b)
(7) (a-b)^2(a+b)^3-(b-a)^2(b+a)^2
原式=(a-b)²(a+b)³-(a-b)²(a+b)²
=(a-b)²(a+b)²(a+b-1)