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

\(24 a^{2} - 27 a = 3 a (8 a - 9)\)

\(10 x y + 12 x = 2 x (5 y + 6)\)

\(6 p q + 27 p r = 3 p (2 q + 9 r)\)

\(20 x y z + 35 x y = 5 x y (4 z + 7)\)

\(4 x^{4} - 14 x^{3} = 2 x^{3} (2 x - 7)\)

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

\(8 a b^{3} + 28 a^{4} b^{2} = 4 a b^{2} (2 b + 7 a^{3})\)

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

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

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

\(a^{10} - 9 = (a^{5} - 3) (a^{5} + 3)\)

\(50 a^{2} - 2 = 2 (25 a^{2} - 1) = 2 (5 a - 1) (5 a + 1)\)

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

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

\(3 p^{10} - 48 p^{2} = 3 p^{2} (p^{8} - 16) = 3 p^{2} (p^{4} - 4) (p^{4} + 4) = 3 p^{2} (p^{2} - 2) (p^{2} + 2) (p^{4} + 4)\)

\(x^{10} y^{8} - 16 z^{12} = (x^{5} y^{4} - 4 z^{6}) (x^{5} y^{4} + 4 z^{6})\)

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

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

\(p^{2} - 13 p + 36 = (p - 4) (p - 9)\)

\(x^{2} - 14 x + 49 = (x - 7) (x - 7)\)

\(5 x^{4} - 50 x^{3} + 80 x^{2} = 5 x^{2} (x^{2} - 10 x + 16) = 5 x^{2} (x - 2) (x - 8)\)

\(a^{12} + 14 a^{6} + 48 = (a^{6} + 6) (a^{6} + 8)\)

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

\(x^{2} + 19 x + 19 = (x + 9\frac{1}{2})^{2} - 90\frac{1}{4} + 19\)

\(\text{} = (x + 9\frac{1}{2})^{2} - 71\frac{1}{4}\)

\(-5 x^{2} + 10 x + 9 = -5 (x^{2} - 2 x) + 9\)

\(\text{} = -5 ((x - 1)^{2} - 1) + 9\)

\(\text{} = -5 (x - 1)^{2} + 5 + 9\)
\(\text{} = -5 (x - 1)^{2} + 14\)