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

\(14 a^{2} - 18 a = 2 a (7 a - 9)\)

\(10 x y + 14 x = 2 x (5 y + 7)\)

\(10 x y + 35 x z = 5 x (2 y + 7 z)\)

\(12 p q r + 21 p q = 3 p q (4 r + 7)\)

\(6 a^{3} - 27 a^{4} = 3 a^{3} (2 - 9 a)\)

\(4 p^{7} + 5 p^{6} + p^{5} = p^{5} (4 p^{2} + 5 p + 1)\)

\(10 x^{2} y^{5} + 18 x^{5} y^{4} = 2 x^{2} y^{4} (5 y + 9 x^{3})\)

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

\(25 a^{2} - 64 = (5 a - 8) (5 a + 8)\)

\(144 - 25 x^{2} = (12 - 5 x) (12 + 5 x)\)

\(16 a^{12} - 121 = (4 a^{6} - 11) (4 a^{6} + 11)\)

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

\(45 a^{3} - 20 a = 5 a (9 a^{2} - 4) = 5 a (3 a - 2) (3 a + 2)\)

\(p^{8} - 16 = (p^{4} - 4) (p^{4} + 4) = (p^{2} - 2) (p^{2} + 2) (p^{4} + 4)\)

\(2 x^{5} - 162 x = 2 x (x^{4} - 81) = 2 x (x^{2} - 9) (x^{2} + 9) = 2 x (x - 3) (x + 3) (x^{2} + 9)\)

\(a^{2} b^{12} - 4 c^{8} = (a b^{6} - 2 c^{4}) (a b^{6} + 2 c^{4})\)

\(a^{2} + 8 a + 12 = (a + 2) (a + 6)\)

\(a^{2} - 5 a - 14 = (a - 7) (a + 2)\)

\(x^{2} - 6 x + 8 = (x - 2) (x - 4)\)

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

\(5 x^{4} + 20 x^{3} + 15 x^{2} = 5 x^{2} (x^{2} + 4 x + 3) = 5 x^{2} (x + 3) (x + 1)\)

\(a^{10} - 2 a^{5} - 48 = (a^{5} - 8) (a^{5} + 6)\)

\(x^{2} - 17 x = (x - 8\frac{1}{2})^{2} - 72\frac{1}{4}\)

\(x^{2} - 15 x + 16 = (x - 7\frac{1}{2})^{2} - 56\frac{1}{4} + 16\)

\(\text{} = (x - 7\frac{1}{2})^{2} - 40\frac{1}{4}\)

\(3 x^{2} + 3 x - 11 = 3 (x^{2} + x) - 11\)

\(\text{} = 3 ((x + \frac{1}{2})^{2} - \frac{1}{4}) - 11\)

\(\text{} = 3 (x + \frac{1}{2})^{2} - \frac{3}{4} - 11\)
\(\text{} = 3 (x + \frac{1}{2})^{2} - 11\frac{3}{4}\)