【数学】分组分解法

题目

【数学】分组分解法
把下列各式分解因式：
(1)x^2-2x+1-25y^2
(2)36a^2-25b^2-10b-1
(3)b^2+4a-1-4a^2
(4)x^2-2xy+y^2+ax-ay
(5)x^2-4xy+4y^2-2x+4y
(6)3a^2-3ab+2ab-2b^2-a+b
(7)ax^2+bx^2+bx+ax+cx^2+cx
(8)x^2-12xy+36y^2-6x+36y+8

答案

(1)=(x-1)^2-(5y)^2=(x-1-5y)(x-1+5y)
(2)=(6A)^2-(5b+1)^2=(6a-5b-1)(6a+5b+1)
(3)=b^2-(2a-1)^2=(b-2a+1)(b+2a-1)
(4)=(x-y)^2-a(x-y)=(x-y)(x-y-a)
(5)=(x-2y)^2-2(x-2y)=(x-2y)(x-2y-2)
(6)=3a^2-ab-2b^2-a+b=(a-b)(3a+2b)-(a-b)=(a-b)(3a+2b-1)
(7)=ax(x+1)+bx(x+1)+cx(x+1)=(x+1)(ax+bx+cx)=x(x+1)(a+b+c)
(8)=(x-6y)^2-6(x-6y)+8=[(x-6y)-4][(x-6y)-2]