Ontbinden in factoren

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

\(6 a^{2} - 21 a = 3 a (2 a - 7)\)

\(20 a b + 25 a = 5 a (4 b + 5)\)

\(8 p q + 18 p r = 2 p (4 q + 9 r)\)

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

\(15 p^{4} - 27 p^{3} = 3 p^{3} (5 p - 9)\)

\(8 p + 9 p^{3} + p^{5} = p (8 + 9 p^{2} + p^{4})\)

\(10 x^{5} y^{3} + 25 x y^{2} = 5 x y^{2} (2 x^{4} y + 5)\)

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

\(x^{2} + 16 x - 19 = (x + 8)^{2} - 64 - 19\)

\(\text{} = (x + 8)^{2} - 83\)

\(-3 x^{2} + 15 x - 14 = -3 (x^{2} - 5 x) - 14\)

\(\text{} = -3 ((x - 2\frac{1}{2})^{2} - 6\frac{1}{4}) - 14\)

\(\text{} = -3 (x - 2\frac{1}{2})^{2} + 18\frac{3}{4} - 14\)
\(\text{} = -3 (x - 2\frac{1}{2})^{2} + 4\frac{3}{4}\)

\(p^{2} + 15 p + 54 = (p + 6) (p + 9)\)

\(p^{2} + 4 p - 32 = (p + 8) (p - 4)\)

\(a^{2} - 11 a + 28 = (a - 7) (a - 4)\)

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

\(x^{5} - 8 x^{4} + 7 x^{3} = x^{3} (x^{2} - 8 x + 7) = x^{3} (x - 1) (x - 7)\)

\(a^{10} + 7 a^{5} + 6 = (a^{5} + 6) (a^{5} + 1)\)

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

\(144 p^{2} - 49 = (12 p - 7) (12 p + 7)\)

\(4 - 25 a^{2} = (2 - 5 a) (2 + 5 a)\)

\(9 a^{8} - 25 = (3 a^{4} - 5) (3 a^{4} + 5)\)

\(48 a^{2} - 3 = 3 (16 a^{2} - 1) = 3 (4 a - 1) (4 a + 1)\)

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

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

\(2 a^{15} - 162 a^{3} = 2 a^{3} (a^{12} - 81) = 2 a^{3} (a^{6} - 9) (a^{6} + 9) = 2 a^{3} (a^{3} - 3) (a^{3} + 3) (a^{6} + 9)\)

\(x^{12} y^{6} - 121 z^{8} = (x^{6} y^{3} - 11 z^{4}) (x^{6} y^{3} + 11 z^{4})\)