因式分解:a的平方-4a-4b的平方+4b+3

更新时间2019-10-05 04:20:58

a²-4a-4b²+4b+3

=a²-4a+4-4b²+4b-1

=a²-4a+4-(4b²-4b+1)

=(a-2)²-(2b-1)²

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

=(a+2b-3)(a-2b-1)

解；拆常数项

a^2-4a-4b^2+4b+3

=a^2-4a-4b^2+4b+4-1

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

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

=(a-2+2b-1)(a-2-2b+1）

=（a+2b-3)(a-2b-1)

a²-4a-4b²+4b+3

=(a²-4a+4)-(4b²-4b+1)

=(a-2)²-(2b-1)²

=[(a-2)+(2b-1)]*[(a-2)-(2b-1)]

=(a+2b-3)(a-2b-1)