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