1. (x + y)2 - 6(x + y) + 9 = (x + y)2 - 2(x + y).3 + 32 = (x + y - 3)2
2. 4 - 36x + 81x2 = 22 - 2.4.9x + (9x)2 = (2 - 9x)2
3. 9x2 - 24xy + 15y2 = (3x)2 - 2.3x.4y + (4y)2 - y2 = (3x - 4y)2 - y2
= (3x - 4y - y)(3x - 4y + y) = (3x - 5y)(3x - 3y) = 3(x - y)(3x - 5y)
4. a2 - 25b2 + 50bc - 25c2 = a2 - [(5b)2 - 2.5b.5c + (5c)2]
= a2 - (5b - 5c)2 = (a - 5b + 5c)(a + 5b - 5c)