数学因式分解四道（3)

来源：百度知道 编辑：UC知道 时间：2024/06/04 19:01:34
1.a^2-2ab+b^2-c^2
2. 1-x^2-2xy-y^2
3.9·x^2 -6xy+y^2-a^2
4.x^2-9·a^2+12a-4

.a^2-2ab+b^2-c^2
=(a-b)^2-c^2
=(a-b-c)(a-b+c)
1-x^2-2xy-y^2
=1-(x^2+2xy+y^2)
=1-(x+y)^2
=(1+x+y)(1-x-y)
9·x^2 -6xy+y^2-a^2
=(3x-y)^2-a^2
=(3x-y-a)(3x-y+a)
x^2-9·a^2+12a-4
=x^2-(9a^2-12a+4)
=x^2-(3a-2)^2
=(x-3a+2)(x+3a-2)

(a-b)^2-c^2=(a-b+c)(a-b-c)
1-(x+y)^2=(1+x+y)(1-x-y)
(3x-y)^2-a^2=(3x-y+a)(3x-y-a)
x^2-(3a-2)^2=(x-3a+2)(x+3a-2)

1.原式=(A-B)^2-C^2=(A-B+C)(A-B-C)
2.原式=1-(X+Y)^2=(1-X-Y)(1+X+Y)
3.原式=(3X-Y)^2-A^2=(3X-Y-A)(3X-Y+A)
4.原式=(X-3A)(X+3A)-4(X-3A)=(X-3A)(X+3A-4)
第4的最后应该是12A-4X吧,否则做不了啊好象