$a) x^{2} - 25 = (x - 5) (x + 5)$

$b) x^{2} - 3 = (x - 3) (x + 3)$

$c) 4 x^{2} - 1 = (2 x - 1) (2 x + 1)$

$d) 9 - 2 x^{2} = (3 - 2 x) (3 + 2 x)$

$e) x^{2} + 6 x + 9 = x^{2} + 2 \cdot 3 x + 3^{2} = (x + 3)^{2}$

$f) 25 x^{2} - 20 x + 4 = (5 x)^{2} - 2 \cdot 5 x \cdot 2 + 2^{2} = (5 x - 2)^{2}$

$g) (3 x + 4)^{2} - 4 = (3 x + 4)^{2} - 2^{2} = (3 x + 4 - 2) (3 x + 4 + 2) =$

$= (3 x + 2) (3 x + 6) = (3 x + 2) \cdot 3 (x + 2) = 3 (x + 2) (3 x + 2)$

$h) (x^{2} + x - 4)^{2} - (x + 5)^{2} = (x^{2} + x - 4 - (x + 5)) (x^{2} + x - 4 + (x + 5)) =$

$= (x^{2} + x - 4 - x - 5) (x^{2} + x - 4 + x + 5) = (x^{2} - 9) (x^{2} + 2 x + 1) =$

$= (x^{2} - 3^{2}) (x^{2} + 2 x + 1) = (x - 3) (x + 3) (x + 1)^{2}$

$i) a^{4} - b^{4} = (a^{2})^{2} - (b^{2})^{2} = (a^{2} - b^{2}) (a^{2} + b^{2}) = (a - b) (a + b) (a^{2} + b^{2})$

$j) a^{2} + b^{2} - c^{2} - 2 a b = a^{2} - 2 a b + b^{2} - c^{2} = (a - b)^{2} - c^{2} = (a - b - c) (a - b + c)$

$k) x^{3} - 8 = x^{3} - 2^{3} = (x - 2) (x^{2} + 2 x + 2^{2}) = (x - 2) (x^{2} + 2 x + 4)$

$l) a^{3} + 1 = a^{3} + 1^{3} = (a + 1) (a^{2} - a + 1^{2}) = (a + 1) (a^{2} - a + 1)$

$m) (x + 1)^{3} - (x - 1)^{3} = (x + 1 - (x - 1)) ((x + 1)^{2} + (x + 1) (x - 1) + (x - 1)^{2}) =$

$= (x + 1 - x + 1) (x^{2} + 2 x + 1 + x^{2} - 1 + x^{2} - 2 x + 1) = 2 (3 x^{2} + 1)$

$n) a^{4} + b^{4} = (a^{2} + b^{2})^{2} - 2 a^{2} b^{2} = (a^{2} + b^{2} - 2 a b) (a^{2} + b^{2} + 2 a b)$