Question

初二数学题，用提公因式法做

(1) x^4-x^3y (2)2ab+6b (3)5x^2y+10xy^2-15xy (4)3x(m-n)+2(m-n)
(5)3(x-3)^2-6(3-x) (6)y^2(2x+1)+y(2x+1)^2 (7)a^2b(a-b)+3ab(a-b)
要过程的，过程没我主要看过程

Answer 1

1. x^4-x^3y=x^3*x-x^3*y=x^3(x-y)
2. 2ab+6b=2ba+3*2b=2b(a+3)
3. 原式=5(x^2*y+2x*y^2+3xy)=5xy(x+y-3)
4. 原式=(3x+2)(m-n) 小学的减法移项
5.原式= 3(x-3)^2+6(x-3)=(x-3)(3(x-3)+6)=(x-3)(3x-3) 换号变项
6.原式=y(2x+1)(y+2x+1)
7.原式=(a-b)(a^2*b+3ab)=ab(a-b)(a+3)

记得在x^4-x^3y 是这样打 x^4-x^3*y x^3y是X的3y次方，你们初二还没学这样的幂次方的因式分解吧

Answer 2

(1) x^4-x^3y
=x^3(x-y)
(2)2ab+6b
=2b(a+3)
(3)5x^2y+10xy^2-15xy
=5xy(x+2y-3)
(4)3x(m-n)+2(m-n)
=(m-n)(3x+2)
(5)3(x-3)^2-6(3-x)
=3(x-3)[(x-3)+2]
=3(x-3)(x-1)
(6)y^2(2x+1)+y(2x+1)^2
=y(2x+1)(y+2x+1)
(7)a^2b(a-b)+3ab(a-b)
=ab(a-b)(a+3)

Answer 3

X的平方*4-X的平方*3y
=X的平方*（4-3Y)

2ab+6b
=2b(a+3b）

5XY(x*5/2Y2y5/2-3)

3xm-3xn+2m-2n

Answer 4

(1) x^4-x^3y
=x³(x-y)

(2)2ab+6b
=2b(a+3)

(3)5x^2y+10xy^2-15xy
=5xy(x+2y-3)

(4)3x(m-n)+2(m-n)
=(m-n)(3x+2)

(5)3(x-3)^2-6(3-x)
=3(x-3)²+6(x-3)
=3(x-3)(x-1)

(6)y^2(2x+1)+y(2x+1)^2
=y(2x+1)(y+2x+1)

(7)a^2b(a-b)+3ab(a-b)
=ab(a-b)(a+3)