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

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

\(16 a b + 36 a = 4 a (4 b + 9)\)

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

\(10 p q r + 14 p q = 2 p q (5 r + 7)\)

\(15 p^{4} + 24 p^{5} = 3 p^{4} (5 + 8 p)\)

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

\(12 a^{2} b^{2} + 32 a^{5} b^{4} = 4 a^{2} b^{2} (3 + 8 a^{3} b^{2})\)

\(x^{2} - 121 = (x - 11) (x + 11)\)

\(25 a^{2} - 9 = (5 a - 3) (5 a + 3)\)

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

\(81 x^{12} - 49 = (9 x^{6} - 7) (9 x^{6} + 7)\)

\(75 p^{2} - 3 = 3 (25 p^{2} - 1) = 3 (5 p - 1) (5 p + 1)\)

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

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

\(p^{6} - 81 p^{2} = p^{2} (p^{4} - 81) = p^{2} (p^{2} - 9) (p^{2} + 9) = p^{2} (p - 3) (p + 3) (p^{2} + 9)\)

\(a^{10} b^{12} - 81 c^{12} = (a^{5} b^{6} - 9 c^{6}) (a^{5} b^{6} + 9 c^{6})\)

\(p^{2} + 9 p + 14 = (p + 7) (p + 2)\)

\(a^{2} + 2 a - 24 = (a + 6) (a - 4)\)

\(x^{2} - 10 x + 24 = (x - 4) (x - 6)\)

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

\(2 a^{5} - 28 a^{4} + 90 a^{3} = 2 a^{3} (a^{2} - 14 a + 45) = 2 a^{3} (a - 9) (a - 5)\)

\(x^{6} - x^{3} - 30 = (x^{3} - 6) (x^{3} + 5)\)

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

\(x^{2} + 2 x - 16 = (x + 1)^{2} - 1 - 16\)

\(\text{} = (x + 1)^{2} - 17\)

\(3 x^{2} + 6 x - 13 = 3 (x^{2} + 2 x) - 13\)

\(\text{} = 3 ((x + 1)^{2} - 1) - 13\)

\(\text{} = 3 (x + 1)^{2} - 3 - 13\)
\(\text{} = 3 (x + 1)^{2} - 16\)