因式分解:(1)a^2-b^2-a-b(2)4x^2+4x-y^2+1

问题描述:

因式分解:(1)a^2-b^2-a-b(2)4x^2+4x-y^2+1

  1. a^2-b^2-a-b=(a-b)(a+b)-(a+b)=(a-b-1)(a+b)

  2. 4x^2+4x-y^2+1=(2x+1)^2-y^2=(2x+y+1)(2x-y+1)

a^2-b^2-a-b
=(a+b)(a-b)-(a+b)
=(a+b)(a-b-1)
4x^2+4x-y^2+1
=(4x^2+4x+1)-y^2
=(2x+1)^2-y^2
=(2x+1+y)(2x+1-y)
=(2x+y+1)(2x-y+1)