Question

因式分解：x2－9a2＋12a－4；x2y+3xy2-x-3y；1-x2-2xy-y2；3a2+2b-2ab-3a；x2+y2+2xy+ax+ay；3x4-48y4

8a3-4a2-2a+1；x2-3xy-28y2；(x2-x)^2-4(x2-x)-12

Answer 1

x2－9a2＋12a－4=x2-[(3a)2-2*3a*2+4]=x2-(3a-2)^2=(x+3a-2)(x-3a+2)
x2y+3xy2-x-3y=xy(x+3y)-(x+3y)=(xy-1)(x+3y)
1-x2-2xy-y2=1-(x+y)^2=(1+x+y)(1-x-y)
3a2+2b-2ab-3a=3a(a-1)-2b(a-1)=(3a-2b)(a-1)
x2+y2+2xy+ax+ay=(x+y)^2+a(x+y)=(x+y)(x+y+a)
3x4-48y4=3(x^4-16y^4)=3(x^2+4y^2)(x+2y)(x-2y)

追问

还有8a3-4a2-2a+1；x2-3xy-28y2；(x2-x)^2-4(x2-x)-12

追答

sorry，没看见……
8a3-4a2-2a+1=4a2(2a-1)-(2a-1)=(4a2-1)(2a-1)=(2a+1)(2a-1)^2
x2-3xy-28y2=(x-7y)(x+4y)（十字相乘知道吧）
(x2-x)^2-4(x2-x)-12把x2-x看成整体：原式=(x2-x+2)(x2-x-6)=(x+2)^2(x-1)(x-3)

Answer 2

x2，x2，y2是啥意思啊，平方吗

追问

x的平方，y的平方