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

\(6 x^{2} + 8 x = 2 x (3 x + 4)\)

\(18 p q + 21 p = 3 p (6 q + 7)\)

\(6 a b + 14 a c = 2 a (3 b + 7 c)\)

\(28 x y z + 32 x y = 4 x y (7 z + 8)\)

\(12 x^{3} + 32 x^{4} = 4 x^{3} (3 + 8 x)\)

\(2 p^{4} - 7 p + p^{8} = p (2 p^{3} - 7 + p^{7})\)

\(12 x^{5} y^{4} + 15 x y^{5} = 3 x y^{4} (4 x^{4} + 5 y)\)

\(a^{2} - 100 = (a - 10) (a + 10)\)

\(64 a^{2} - 49 = (8 a - 7) (8 a + 7)\)

\(25 - 49 x^{2} = (5 - 7 x) (5 + 7 x)\)

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

\(75 p^{2} - 48 = 3 (25 p^{2} - 16) = 3 (5 p - 4) (5 p + 4)\)

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

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

\(2 x^{9} - 32 x = 2 x (x^{8} - 16) = 2 x (x^{4} - 4) (x^{4} + 4) = 2 x (x^{2} - 2) (x^{2} + 2) (x^{4} + 4)\)

\(a^{8} b^{12} - 121 c^{10} = (a^{4} b^{6} - 11 c^{5}) (a^{4} b^{6} + 11 c^{5})\)

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

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

\(x^{2} - 10 x + 21 = (x - 3) (x - 7)\)

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

\(5 a^{4} - 5 a^{3} - 150 a^{2} = 5 a^{2} (a^{2} - a - 30) = 5 a^{2} (a + 5) (a - 6)\)

\(a^{14} + 7 a^{7} + 10 = (a^{7} + 2) (a^{7} + 5)\)