\(a^{2} + 2 a = a (a + 2)\)

\(12 x^{2} - 28 x = 4 x (3 x - 7)\)

\(16 x y + 28 x = 4 x (4 y + 7)\)

\(14 p q + 18 p r = 2 p (7 q + 9 r)\)

\(12 a b c + 14 a b = 2 a b (6 c + 7)\)

\(8 x^{2} + 14 x^{5} = 2 x^{2} (4 + 7 x^{3})\)

\(2 a^{2} - 3 a^{6} + a^{3} = a^{2} (2 - 3 a^{4} + a)\)

\(21 x^{2} y^{2} + 24 x^{4} y^{3} = 3 x^{2} y^{2} (7 + 8 x^{2} y)\)

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

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

\(25 - 81 a^{2} = (5 - 9 a) (5 + 9 a)\)

\(16 a^{10} - 9 = (4 a^{5} - 3) (4 a^{5} + 3)\)

\(36 x^{2} - 4 = 4 (9 x^{2} - 1) = 4 (3 x - 1) (3 x + 1)\)

\(3 x^{5} - 12 x^{3} = 3 x^{3} (x^{2} - 4) = 3 x^{3} (x - 2) (x + 2)\)

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

\(3 a^{9} - 48 a = 3 a (a^{8} - 16) = 3 a (a^{4} - 4) (a^{4} + 4) = 3 a (a^{2} - 2) (a^{2} + 2) (a^{4} + 4)\)

\(a^{10} b^{4} - 9 c^{4} = (a^{5} b^{2} - 3 c^{2}) (a^{5} b^{2} + 3 c^{2})\)

\(x^{2} + 10 x + 24 = (x + 6) (x + 4)\)

\(p^{2} - 6 p - 16 = (p - 8) (p + 2)\)

\(a^{2} - 14 a + 45 = (a - 5) (a - 9)\)

\(x^{2} - 10 x + 25 = (x - 5) (x - 5)\)

\(a^{4} + a^{3} - 72 a^{2} = a^{2} (a^{2} + a - 72) = a^{2} (a + 9) (a - 8)\)

\(p^{6} - 5 p^{3} - 14 = (p^{3} + 2) (p^{3} - 7)\)

\(x^{2} - 3 x = (x - 1\frac{1}{2})^{2} - 2\frac{1}{4}\)

\(x^{2} - 18 x + 18 = (x - 9)^{2} - 81 + 18\)

\(\text{} = (x - 9)^{2} - 63\)

\(-3 x^{2} + 3 x + 14 = -3 (x^{2} - x) + 14\)

\(\text{} = -3 ((x - \frac{1}{2})^{2} - \frac{1}{4}) + 14\)

\(\text{} = -3 (x - \frac{1}{2})^{2} + \frac{3}{4} + 14\)
\(\text{} = -3 (x - \frac{1}{2})^{2} + 14\frac{3}{4}\)