Question

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

Answer 1

(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)

Answer 2

2、原式=6mx-nx²-nx²=2x（3m-nx）
3、原式=2-5（9x²-12x+4）+3x=-45x²+63x-18=-9（5x-2）（x-1)
4、原式=x（b+c-d）+y（b+c-d）-（b+c-d）=（x+y-1）（b+c-d）
5、原式=（3m-2p）（4a-5b+4b-a）=（3m-2p）（3a-b）
6、原式=ab（x-2y）+ac（x-2y）+2ab（x-2y）=a（x-2y）（3b+c）
7、原式=（a-b）²（a+b）³-（a-b）²（a+b）²=（a-b）²（a+b）²（a+b-1）

Answer 3

(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)=6nx
(3) : 2-5(3x-2)^2+3x =2-5(9x^2-12x+4)+3x=-45x^2-57x+22(自已用公式解吧)
(4) x(b+c-d)-y(d-b-c)-b-c+d=x(b+c-d)+y(b+c-d)+(b+c-d)=(b+c-d)(x+y+1)
(5) (4a-5b)(3m-2p)+(4b-a)(3m-2p)=((4a-5b)+(4b-a))(3m-2p)=)=(4a-5b+4b-a)(3m-2p)=(3a-b)(3m-2p)
(6) ab(x-2y)-ac(2y-x)+ab(2x-4y)= ab(x-2y)+ac(x-2y)+2ab(x-2y)=(ab+ac+2ab)(x-2y)=a(a+c+2b)(x-2y)
(7) (a-b)^2(a+b)^3-(b-a)^2(b+a)^2=(a-b)^2(a+b)^3+(a-b)^2(a+b)^2==(a-b)^2(a+b)^2((a+b)+1)=
(a-b)^2(a+b)^2(a+b+1)