a) = (5x)^2 - 1 = (5x - 1)(5x + 1)
b) = (3x)^3 + 2^3 = (3x + 2)(9x^2 - 6x + 4)
c) = x^3 - (5y)^3 = (x - 5y)(x^2 + 5xy + 25y^2)
d) = x^2 + 12x + 36 = x^2 + 2.6.x + 6^2 = (x + 6)^2
e) = (x^2 - y^2) + (3x + 3y)
= (x - y)(x + y) + 3(x + y)
= (x - y + 3)(x + y)
g) = x^2 + 2xy + y^2 + (5x + 5y)
= (x + y)^2 + 5(x + y)
= (x + y)(x + y + 5)
h) = (x^2 - 2xy + y^2) - (x - y)
= (x - y)^2 - (x - y)
= (x - y)(x - y - 1)
i) = x^3 + y^3 + (x^2 - xy + y^2)
= (x + y)(x^2 - xy + y^2) + .....................
= (x + y + 1)(x^2 - xy + y^2)
m) = (x^3 - y^3) + (x^2 + xy + y^2)
= (x - y)(x^2 + xy + y^2) + _____________
= (x - y + 1)(x^2 + xy + y^2)
n) = x(y - 2x) + (y^2 - 4x^2)
= x(y - 2x) + (y - 2x)(y + 2x)
= (x + y + 2x)(y - 2x)
= (3x + y)(y - 2x)
k) = x(y + x) + 7(x + y)
= (x + 7)(x + y)
p) = x^2 - (y^2 - 6y + 9)
= x^2 - (y - 3)^2
= (x - y + 3)(x + y - 3)