\(x^{2} + 5 x = x (x + 5)\)

\(8 p^{2} - 36 p = 4 p (2 p - 9)\)

\(21 x y + 27 x = 3 x (7 y + 9)\)

\(12 a b + 28 a c = 4 a (3 b + 7 c)\)

\(15 a b c + 25 a b = 5 a b (3 c + 5)\)

\(9 a^{3} + 21 a^{2} = 3 a^{2} (3 a + 7)\)

\(2 a^{5} + 5 a^{8} + a = a (2 a^{4} + 5 a^{7} + 1)\)

\(10 p q + 18 p^{5} q^{4} = 2 p q (5 + 9 p^{4} q^{3})\)

\(x^{2} - 121 = (x - 11) (x + 11)\)

\(36 x^{2} - 25 = (6 x - 5) (6 x + 5)\)

\(81 - 100 x^{2} = (9 - 10 x) (9 + 10 x)\)

\(100 p^{14} - 49 = (10 p^{7} - 7) (10 p^{7} + 7)\)

\(36 x^{2} - 100 = 4 (9 x^{2} - 25) = 4 (3 x - 5) (3 x + 5)\)

\(75 a^{3} - 12 a = 3 a (25 a^{2} - 4) = 3 a (5 a - 2) (5 a + 2)\)

\(a^{8} - 81 = (a^{4} - 9) (a^{4} + 9) = (a^{2} - 3) (a^{2} + 3) (a^{4} + 9)\)

\(2 a^{5} - 32 a = 2 a (a^{4} - 16) = 2 a (a^{2} - 4) (a^{2} + 4) = 2 a (a - 2) (a + 2) (a^{2} + 4)\)

\(x^{4} y^{4} - 16 z^{10} = (x^{2} y^{2} - 4 z^{5}) (x^{2} y^{2} + 4 z^{5})\)

\(p^{2} + 11 p + 24 = (p + 3) (p + 8)\)

\(x^{2} - 3 x - 18 = (x - 6) (x + 3)\)

\(a^{2} - 4 a + 3 = (a - 1) (a - 3)\)

\(x^{2} - 12 x + 36 = (x - 6) (x - 6)\)

\(2 a^{3} - 10 a^{2} - 48 a = 2 a (a^{2} - 5 a - 24) = 2 a (a - 8) (a + 3)\)

\(a^{6} + 2 a^{3} - 35 = (a^{3} + 7) (a^{3} - 5)\)

\(x^{2} + 6 x = (x + 3)^{2} - 9\)

\(x^{2} - 14 x - 2 = (x - 7)^{2} - 49 - 2\)

\(\text{} = (x - 7)^{2} - 51\)

\(4 x^{2} + 20 x + 9 = 4 (x^{2} + 5 x) + 9\)

\(\text{} = 4 ((x + 2\frac{1}{2})^{2} - 6\frac{1}{4}) + 9\)

\(\text{} = 4 (x + 2\frac{1}{2})^{2} - 25 + 9\)
\(\text{} = 4 (x + 2\frac{1}{2})^{2} - 16\)