a) (x + y)^2 - 25 = (x + y + 5)( x + y - 5)
b) 1 - 2y + y^2 = (y - 2)^2
c) 4x^2 + 8xy - 3x - 6y = 4x(x + 2) - 3(x + 2) = (4x - 3)(x + 2)
d) 2x^2 + 2y^2 -x^2.z + z - y^2.z - 2
= (2x^2 - x^2.z) + (2y^2 - y^2.z) + ( z - 2)
= x^2. (2 - z) + y^2.(2 - z) - (2 - z)
= (2 - z)(x^2 + y^2 - 1)
e) 27 + 27x + 9x^2 + x^3 = (x + 3)^2
g) 8 - 27x^3 = (2 - 3x)(4 + 6x + 9x^2)