几道简单的因式分解题~

题目

几道简单的因式分解题~
(1) (2x-3y)^2 - 4a^2
(2) x^4 - 2x^2 + 1
(3) x^2 - a^2 - 2x - 2a
(4) 4x^2 - 4xy + y^2 - a^2
(5) (x + y)^2 - 2(x + y ) - 3
(6) x^2 - 2xy -3y^2 + x + y

答案

(1) (2x-3y)^2 - 4a^2
=(2x-3y+2a)(2x-3y-2a)
(2) x^4 - 2x^2 + 1
=(x^2-1)^2
=(x+1)^2(x-1)^2
(3) x^2 - a^2 - 2x - 2a
=(x+a)(x-a)-2(x+a)
=(x+a)(x-a-2)
(4) 4x^2 - 4xy + y^2 - a^2
=(2x-y)^2-a^2
=(2x-y+a)(2x-y-a)
(5) (x + y)^2 - 2(x + y ) - 3
=(x+y-3)(x+y+1)
(6) x^2 - 2xy -3y^2 + x + y
=(x-3y)(x+y)+(x+y)
=(x+y)(x-3y+1)