因式分解：x^2-4(2y-5)x+4(2y-5)^2+2x-8y+21_数学解答

因式分解：x^2-4(2y-5)x+4(2y-5)^2+2x-8y+21

人气：354 ℃　时间：2019-10-06 23:22:36

解答

设2y-5=t
x^2-4tx+4t^2+2x-4(2y-5)-20+21
=x^2-4tx+4t^2+2x-4t+1
=x^2-(4t-2)x+4t^2-4t+1
=x^2-2(2t-1)x+(2t-1)^2
=(x-2t+1)^2
=(x-2(2y-5)+1)^2
=(x-4y+11)^2