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

\(15 a^{2} - 27 a = 3 a (5 a - 9)\)

\(6 x y + 8 x = 2 x (3 y + 4)\)

\(4 x y + 10 x z = 2 x (2 y + 5 z)\)

\(35 p q r + 40 p q = 5 p q (7 r + 8)\)

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

\(3 p^{2} - 7 p^{6} + p = p (3 p - 7 p^{5} + 1)\)

\(20 a b^{5} + 24 a^{4} b = 4 a b (5 b^{4} + 6 a^{3})\)

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

\(100 x^{2} - 81 = (10 x - 9) (10 x + 9)\)

\(25 - 144 a^{2} = (5 - 12 a) (5 + 12 a)\)

\(81 x^{6} - 100 = (9 x^{3} - 10) (9 x^{3} + 10)\)

\(50 p^{2} - 32 = 2 (25 p^{2} - 16) = 2 (5 p - 4) (5 p + 4)\)

\(45 a^{3} - 5 a = 5 a (9 a^{2} - 1) = 5 a (3 a - 1) (3 a + 1)\)

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

\(3 a^{14} - 243 a^{2} = 3 a^{2} (a^{12} - 81) = 3 a^{2} (a^{6} - 9) (a^{6} + 9) = 3 a^{2} (a^{3} - 3) (a^{3} + 3) (a^{6} + 9)\)

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

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

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

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

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

\(3 a^{3} - 24 a^{2} - 27 a = 3 a (a^{2} - 8 a - 9) = 3 a (a + 1) (a - 9)\)

\(p^{14} - 12 p^{7} + 27 = (p^{7} - 3) (p^{7} - 9)\)

\(x^{2} + 15 x = (x + 7\frac{1}{2})^{2} - 56\frac{1}{4}\)

\(x^{2} - 2 x + 10 = (x - 1)^{2} - 1 + 10\)

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

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

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

\(\text{} = -4 (x + \frac{1}{2})^{2} + 1 - 7\)
\(\text{} = -4 (x + \frac{1}{2})^{2} - 6\)