因式分解 a²-b²-c²+2bcab-a-b+1 x²+4xy+4y² 4x^3 y+4x²y²+xy^3

因式分解 a²-b²-c²+2bcab-a-b+1 x²+4xy+4y² 4x^3 y+4x²y²+xy^3
因式分解 a²-b²-c²+2bc
ab-a-b+1 x²+4xy+4y² 4x^3 y+4x²y²+xy^3

因式分解 a²-b²-c²+2bcab-a-b+1 x²+4xy+4y² 4x^3 y+4x²y²+xy^3
a²-b²-c²+2bc
=a²-(b-c)²
=(a+b-c)(a-b+c)
ab-a-b+1
=a(b-1)-(b-1)
=(b-1)(a-1)
x²+4xy+4y²
=(x+2y)²
4x^3 y+4x²y²+xy^3
=xy(4x²+4xy+y²)
=xy(2x+y) ²

a²-b²-c²+2bc＝a²－（b+c）²=(a+b+c)(a-b-c)
ab-a-b+1=a(b-1)-(b-1)=(b-1)(a-1)
x²+4xy+4y²=(x+2y)²
4x^3 y+4x²y²+xy^3(有问题）

a²-b²-c²+2bc
=a^2-(b^2-2bc+c^2)
=a^2-(b-c)^2
=(a+b-c)(a-b+c)
ab-a-b+1
=a(b-1)-(b-1)
=(b-1)(a-1)
x²+4xy+4y²
=(x+2y)^2

4x^3 y+4x²y²+xy^3
=xy(4x^2+4xy+y^2)
=xy(2x+y)^2