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

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

\(24 x y + 28 x = 4 x (6 y + 7)\)

\(8 a b + 36 a c = 4 a (2 b + 9 c)\)

\(20 p q r + 36 p q = 4 p q (5 r + 9)\)

\(20 p^{5} + 32 p^{2} = 4 p^{2} (5 p^{3} + 8)\)

\(4 x^{5} - 7 x^{7} + x = x (4 x^{4} - 7 x^{6} + 1)\)

\(6 x^{4} y^{3} + 15 x^{5} y^{4} = 3 x^{4} y^{3} (2 + 5 x y)\)

\(a^{2} - 144 = (a - 12) (a + 12)\)

\(64 a^{2} - 9 = (8 a - 3) (8 a + 3)\)

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

\(121 x^{12} - 25 = (11 x^{6} - 5) (11 x^{6} + 5)\)

\(18 p^{2} - 32 = 2 (9 p^{2} - 16) = 2 (3 p - 4) (3 p + 4)\)

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

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

\(2 a^{13} - 32 a = 2 a (a^{12} - 16) = 2 a (a^{6} - 4) (a^{6} + 4) = 2 a (a^{3} - 2) (a^{3} + 2) (a^{6} + 4)\)

\(x^{6} y^{8} - 81 z^{4} = (x^{3} y^{4} - 9 z^{2}) (x^{3} y^{4} + 9 z^{2})\)

\(x^{2} + 12 x + 32 = (x + 8) (x + 4)\)

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

\(x^{2} - 17 x + 72 = (x - 9) (x - 8)\)

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

\(5 a^{3} - 50 a^{2} + 105 a = 5 a (a^{2} - 10 a + 21) = 5 a (a - 3) (a - 7)\)

\(a^{12} - 11 a^{6} + 30 = (a^{6} - 6) (a^{6} - 5)\)

\(x^{2} - 12 x = (x - 6)^{2} - 36\)

\(x^{2} + 8 x + 19 = (x + 4)^{2} - 16 + 19\)

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

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

\(\text{} = 4 ((x + \frac{1}{2})^{2} - \frac{1}{4}) + 9\)

\(\text{} = 4 (x + \frac{1}{2})^{2} - 1 + 9\)
\(\text{} = 4 (x + \frac{1}{2})^{2} + 8\)