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

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

\(8 x y + 36 x = 4 x (2 y + 9)\)

\(10 x y + 45 x z = 5 x (2 y + 9 z)\)

\(14 a b c + 18 a b = 2 a b (7 c + 9)\)

\(24 p^{4} - 28 p^{2} = 4 p^{2} (6 p^{2} - 7)\)

\(7 a^{7} + 9 a^{6} + a^{4} = a^{4} (7 a^{3} + 9 a^{2} + 1)\)

\(18 x^{3} y^{4} - 21 x^{4} y^{5} = 3 x^{3} y^{4} (6 - 7 x y)\)

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

\(16 a^{2} - 1 = (4 a - 1) (4 a + 1)\)

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

\(36 p^{6} - 49 = (6 p^{3} - 7) (6 p^{3} + 7)\)

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

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

\(a^{12} - 81 = (a^{6} - 9) (a^{6} + 9) = (a^{3} - 3) (a^{3} + 3) (a^{6} + 9)\)

\(x^{7} - 16 x^{3} = x^{3} (x^{4} - 16) = x^{3} (x^{2} - 4) (x^{2} + 4) = x^{3} (x - 2) (x + 2) (x^{2} + 4)\)

\(a^{8} b^{6} - 49 c^{4} = (a^{4} b^{3} - 7 c^{2}) (a^{4} b^{3} + 7 c^{2})\)

\(a^{2} + 9 a + 18 = (a + 6) (a + 3)\)

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

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

\(x^{2} + 16 x + 64 = (x + 8) (x + 8)\)

\(x^{4} + x^{3} - 30 x^{2} = x^{2} (x^{2} + x - 30) = x^{2} (x + 6) (x - 5)\)

\(a^{8} - 3 a^{4} - 40 = (a^{4} - 8) (a^{4} + 5)\)

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

\(x^{2} + 18 x - 7 = (x + 9)^{2} - 81 - 7\)

\(\text{} = (x + 9)^{2} - 88\)

\(2 x^{2} + 2 x - 17 = 2 (x^{2} + x) - 17\)

\(\text{} = 2 ((x + \frac{1}{2})^{2} - \frac{1}{4}) - 17\)

\(\text{} = 2 (x + \frac{1}{2})^{2} - \frac{1}{2} - 17\)
\(\text{} = 2 (x + \frac{1}{2})^{2} - 17\frac{1}{2}\)