数学解题网

问题描述：

分解因式
x²y²-2xy+1 9-12t+4t² x²/4+xy+y
(x+y)²+6(x+y)+9 a²-2a(b+c)+（b+c）²
4xy²-4x²y²-y³ -a+2a²-a³

问题解答：

x²y²-2xy+1
=(xy-1)²

9-12t+4t²
=(3-2t)²

x²/4+xy+y²
=(x/2+y)²

(x+y)²+6(x+y)+9
=(x+y+3)²

a²-2a(b+c)+（b+c）²
=[a-(b+c)]²
=(a-b-c)²

4xy²-4x²y²-y³
=y²(4x-4x²-y)

-a+2a²-a³
=-a(1-a)²

1.
x^2y^2-2xy+1
=(xy)^2-2xy+1
=[(xy)-1]^2
=(xy-1)^2

2.
9-12t+4t^2=(2t-3)^2

3.
x^2/4+xy+y^2=(x/2+y)^2

4.
(x+y)^2+6(x+y)+9
=[(x+y)+3]^2
=(x+y+3)^2

5.
a^2-2a(b+c)+(b+c)^2
=[a-(b+c)]^2
=(a-b-c)^2

6.
4xy^2-4x^2y^2-y^3=y^2(4x-4x^2-y)

7.
-a+2a^2-a^3
=a(-1+2a-a^2)
=-a(1-2a+a^2)
=-a(a-1)^2