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

\(25 x^{2} - 40 x = 5 x (5 x - 8)\)

\(8 a b + 20 a = 4 a (2 b + 5)\)

\(10 x y + 15 x z = 5 x (2 y + 3 z)\)

\(10 a b c + 15 a b = 5 a b (2 c + 3)\)

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

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

\(10 a^{4} b^{3} + 16 a^{2} b^{4} = 2 a^{2} b^{3} (5 a^{2} + 8 b)\)

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

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

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

\(81 a^{4} - 121 = (9 a^{2} - 11) (9 a^{2} + 11)\)

\(50 p^{2} - 18 = 2 (25 p^{2} - 9) = 2 (5 p - 3) (5 p + 3)\)

\(3 x^{3} - 48 x = 3 x (x^{2} - 16) = 3 x (x - 4) (x + 4)\)

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

\(2 a^{7} - 32 a^{3} = 2 a^{3} (a^{4} - 16) = 2 a^{3} (a^{2} - 4) (a^{2} + 4) = 2 a^{3} (a - 2) (a + 2) (a^{2} + 4)\)

\(p^{12} q^{2} - r^{6} = (p^{6} q - r^{3}) (p^{6} q + r^{3})\)

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

\(x^{2} + 7 x - 8 = (x + 8) (x - 1)\)

\(x^{2} - 11 x + 18 = (x - 9) (x - 2)\)

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

\(2 p^{5} - 10 p^{4} + 12 p^{3} = 2 p^{3} (p^{2} - 5 p + 6) = 2 p^{3} (p - 3) (p - 2)\)

\(x^{4} + 11 x^{2} + 24 = (x^{2} + 8) (x^{2} + 3)\)

\(x^{2} - 11 x = (x - 5\frac{1}{2})^{2} - 30\frac{1}{4}\)

\(x^{2} - x + 19 = (x - \frac{1}{2})^{2} - \frac{1}{4} + 19\)

\(\text{} = (x - \frac{1}{2})^{2} + 18\frac{3}{4}\)

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

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

\(\text{} = -2 (x - \frac{1}{2})^{2} + \frac{1}{2} - 7\)
\(\text{} = -2 (x - \frac{1}{2})^{2} - 6\frac{1}{2}\)